The 21-year-old Slovenia international appeared to be priority number one on Arsenal's striker shortlist, and the Gunners were optimistic of fending off Manchester United and Chelsea's advances to reach an agreement.
Leipzig would have been powerless to stop Arsenal's swoop had the Gunners triggered a reported £55m clause in his former deal, but Sesko believes that staying in the Bundesliga is the best move for his embryonic career at this point.
A gentleman's agreement in Sesko's deal means that a future Premier League move is not entirely off the cards, but if Mikel Arteta is to continue his pursuit of a new number nine for 2024-25, alternative solutions must be sought.
Alexander Isak, Victor Osimhen and Ivan Toney have already been removed from the shortlist for one reason or another, and Arsenal could even abandon their striker search completely to focus on recruiting a new right-winger instead.
However, there are still several intriguing options available at an affordable price, and here, Sports Mole runs the rule over six strikers that Arsenal could target in the coming weeks.
Joshua Zirkzee - Bologna
Now that chances of a deal for Sesko are dead in the water, Arsenal could turn their attention back to Bologna's Joshua Zirkzee, as per The Guardian, but his signing will not come without a few obstacles.
Zirkzee failed to make the grade at Bayern Munich and left for Bologna for just £7.2m in the summer of 2022, but the Dutchman is now poised to be playing Champions League football with the Rossoblu in 2024-25.
The 23-year-old struck 11 goals of his own and set up five more in 34 Serie A outings in 2023-24, helping Bologna achieve a remarkable fifth-placed finish in Serie A, a position sufficient for Champions League qualification thanks to Italy's supreme UEFA coefficient.
A physically imposing target man at 6ft 4in tall, Zirkzee is only contracted to Bologna until the summer of 2026 and could be one of a few Rossoblu players to follow coach Thiago Motta - bound for Juventus - out of the Dall'Ara exit door.
A fee of £34m could apparently be enough to sever the 23-year-old from his Bologna contract due to the existence of a release clause, and with no renewal in sight, the Rossoblu have every reason to cash in from a business standpoint.
However, Arsenal must first fend off the attention of Manchester United, and even if that endeavour is successful, the final boss could arrive in the form of AC Milan, as Zirkzee is supposedly keen to remain in Serie A and has already struck an accord with the Rossoneri on his yearly wage packet.
Dominic Solanke - Bournemouth
Many a Liverpool fan may have been rubbing their eyes in bewilderment at Dominic Solanke's astounding exploits in a Bournemouth shirt in 2023-24, which have attracted the attention of some of the top teams in the land.
The Basingstoke-born striker - once on the books at Chelsea too - averaged a goal every other game in the Premier League campaign, striking 19 in 38 matches and starting 37 on the bounce before dropping to the bench on the final matchday.
An eye for goal, a 6ft 1in figure and an impeccable fitness record surely makes Solanke a manager's dream when searching for an out-and-out centre-forward, and there was even some suggestion that the ex-Liverpool man could force his way into England's Euro 2024 squad, pleas which fell on deaf ears.
Even without a plane ticket to Germany, Solanke is rumoured to have caught the eye of both Arsenal and Tottenham Hotspur, although Arteta's side would have the immediate advantage of Champions League football if a tense two-way fight materialised.
Like Zirkzee, Solanke's Cherries deal - which is active until 2027 - supposedly includes a release clause as well, albeit a slightly pricier one at £65m, the same amount that Arsenal shelled out for Kai Havertz last year.
Furthermore, only select clubs can trigger that option, the identities of which are unknown. However, top Premier League teams competing in Europe are expected to be among them, seemingly positioning Arsenal at the head of the queue.
Serhou Guirassy - Stuttgart
In addition to their unmissable North London derby scraps and potential battle for Solanke's services, Arsenal and Tottenham could also go head-to-head for the right to bring Stuttgart's Serhou Guirassy to the Premier League.
As is the case with Zirkzee, Guirassy also played a fundamental role in one of the surprise Champions League qualifications for 2024-25, propelling Stuttgart to a shock second-placed finish over Bayern Munich with 28 goals in as many Bundesliga matches.
While Harry Kane's record-breaking feats inevitably made more headlines, Guirassy made an equally exceptional start to life in Germany, with no fewer than 10 goals in his first five Bundesliga contests and a six-match scoring sequence from March to April.
Only Kane managed more German top-flight strikes than the Guinea international, who ranks in the top 1% of strikers for non-penalty Expected Goals and Assisted Goals over the past 365 days, averaging nearly one per game.
Also fashioning over two chances per game on average for his teammates, Guirassy would represent a striker who could do it all should he replicate such feats in the Premier League, which can certainly be a tall order.
However, the 28-year-old's Stuttgart contract - which runs until 2026 - reportedly includes a very modest release clause of around £15m, so Arsenal must get in quick if they are to push their way to the front of the queue.
Santiago Gimenez - Feyenoord
Arne Slot's move to Liverpool to fill Jurgen Klopp's boots may be the most high-profile departure from Feyenoord this summer, but attention now turns to the revered Rotterdam stars who could follow him out of the exit door.
Twenty-three-year-old striker Santiago Gimenez is undoubtedly one of them, having continued to go from strength to strength in the Netherlands, notching 26 goals in addition to eight assists across all tournaments in 2023-24.
The Mexico international did not quite do enough to take home the Golden Boot - that accolade was shared between Luuk de Jong and Vangelis Pavlidis - but his prolific exploits were enough to attract glances from some of Europe's big boys regardless.
Feyenoord briefly managed to ward off the vultures by extending Gimenez's contract until 2027 last year, but it is presumably only a matter of time before the 23-year-old is lured to one of the big five European leagues.
However, in what seems to be the theme of this list, Tottenham are also in for the Mexican's signature, as are the likes of Roma and AC Milan, who believe that he could flourish in Serie A.
Of course, Slot joining Liverpool inevitably led to a few fleeting Anfield links too, but the Reds are prioritising other areas of the pitch not thought to be serious contenders right now.
Maximilian Beier - Hoffenheim
One of the true breakthrough stars of the 2023-24 season, Hoffenheim hotshot Maximilian Beier had already made fleeting first-team appearances for the Bundesliga side before it was decided that a loan move down the divisions would be best for his development.
Beier did not set the 2. Bundesliga alight during his two years with Hannover 96, managing a modest 15 goals in 68 games, but whatever Hoffenheim were feeding the 21-year-old in pre-season went down a treat; he bettered that tally in just one campaign this time around.
Indeed, Beier came up with 16 goals in the 2023-24 Bundesliga campaign from a range of positions - playing as a centre-forward, winger and attacking midfielder - and his versatility could also help solve Arteta's wide dilemma, thereby killing two attacking birds with one German stone.
Beier's scintillating form domestically convinced Julian Nagelsmann that he was ready for a Euro 2024 call-up, and he made his senior Germany debut in a friendly draw with Ukraine earlier this month, although Mannschaft starts are likely to be a bridge too far right now.
Nevertheless, the 21-year-old's potential is evident, and having only been cautioned once in the 2023-24 Bundesliga season, his disciplinary record - or lack of - should make him an attractive proposition for Arteta, a yellow-card magnet himself.
However, among the four Premier League clubs rumoured to have registered their interest in Beier - under contract with Hoffenheim until 2027 - Arsenal are not thought to be one of them.
Artem Dovbyk - Girona
Together with fellow Ukrainian Viktor Tsygankov, also believed to have attracted Arsenal's attention over the past few months, Artem Dovbyk was another jewel in the Girona crown during their astonishing La Liga performance last term.
With 24 goals and eight assists under his belt from 36 matches, Dovbyk's contributions were pivotal to Girona's shock Champions League qualification, and he is also set to lead the line for his country at Euro 2024.
Still relatively young at 26 years of age - although he will turn 27 on June 21 - the Ukraine international has four years left to run on his deal with Girona, who shelled out just £6.5m to prise him away from Dnipro-1 last year.
Fewer than 12 months after leaving his homeland, Dovbyk is already the recipient of one Trofeo Pichichi - awarded to the highest scorer in a La Liga campaign - and a move to Chelsea was briefly mooted for the 26-year-old.
Of course, the Blues are also impacted by Sesko's decision to prolong his Leipzig stay and could go back in for Dovbyk after their interest initially cooled, but reports from Spain have suggested that Arsenal are in the picture too.
Another physically intimidating attacker at 6ft 2in tall, Dovbyk is also proficient from the penalty spot and is in the top 1% of strikers for successful take-ons (68%) in Europe's big five leagues over the past year, albeit while attempting far fewer than Gabriel Jesus, Arsenal's resident chaos merchant.