The north London club have reignited their interest in Sesko from last summer, although a mid-season move is still complicated, with his club reluctant to sell.
To make matters more complicated, Sesko's agent has made it clear that a loan move in January is not an option.
However, the Gunners already have a head-start in their pursuit of the £70million-rated striker.
talkSPORT understands Sesko was sold on Arsenal's project last summer, choosing them over Chelsea and United, but decided to stay in Germany and boost his short-term development.
Reflecting on Arsenal's chances of signing the 21-year-old this month, talkSPORT transfer correspondent Ben Jacobs told Inside Gooners: "The good news for Arsenal is that they have a number of concrete summer targets so there is a logic of escalating the pursuit of some of them for January.
READ MORE ON FOOTBALL
I joined Arsenal on deadline day after waking up to two missed calls from Santi Cazorla
'We need help' - Mikel Arteta sends clear message to Arsenal board over January transfers
"It's whether they're feasible, these targets are difficult to get in the market.
"With Sesko, some contact has been made with Leipzig to understand whether anything is possible.
"There's no release cause in his new contract and the player is very keen on his own development to make sure he doesn't rush a move.
"Even though Leipzig are out of the Champions League, they're pushing in the cup and to qualify again next season.
Most read in Football
'Embarrassing!' - talkSPORT host left disgusted by Man United's Alejandro Garnacho stance
Man United need complete overhaul and one player could change their whole team
Tottenham join race to sign striker who is already in talks over move to rivals West Ham
Jamie Carragher in stitches at MOTD legend's claim Gary Neville can save Man United
"It's not impossible but it's difficult and they'll want to protect the relationship with Leipzig if they're to revisit it in the summer.
"The better news for Arsenal is that last summer when the project was pitched from Arsenal, Chelsea and Man United, Sesko picked Arsenal and then made a secondary choice of whether it was now or to stay at Leipzig.
"It's going to take a crazy offer or be impossible in January because Leipzig's position is very firm."
The Slovenia international has scored eight goals and assisted two in the Bundesliga so far this season, as well as scoring four in the Champions League.
He has reached a total of 31 goals in 67 games for Leipzig and previously won three Austrian Bundesliga titles during his time at RB Salzburg.
At individual level, he was named Slovenian Footballer of the Year in 2022, and has won the Slovenian Youth Footballer of the Year title three years in a row from 2021-2023.
Arsenal's need for a striker became more desperate after Gabriel Jesus suffered a cruciate ligament injury which could keep him sidelined for a year.
Many remain unconvinced by first-choice striker Kai Havertz, who has eight goals in 19 Premier League matches this season.
Manager Mikel Arteta recently admitted he is consulting his own players over who the Gunners should sign in January.
Arteta said: "We have very, very short numbers for many, many weeks and they recognise the situation, we all do. That's why we are trying to do what is right for the club, the team, that's our intention."
He added: "I always do it, especially if they know them because that's getting us away from the computer and what the data is saying and it is real," he said.
"I have seen it, I sense it. A player can score a lot of goals, great. How does this player react when he hasn't scored for six or seven games? This is what I am interested in.
Read More on talkSPORT
Patrick Mahomes' game-winner in Chiefs-Bills classic led to major NFL rule change
Fans stunned to learn Jeff Bezos' fiancée has child with Chiefs star who works for Amazon
"What kind of goals does he score? Against which teams, in which context? Is it first half or second half? Is it only with his right foot, only headers, only in open spaces? Does he like the physical contact of this league?
"There are a lot of things. So when you have a player that has spent a lot of days with him, that is really valuable information to have."