The Ghana international has been one of the standout stars of the Cherries' season and was a constant threat in Bournemouth's memorable 2-0 win over a 10-man Arsenal side on Saturday evening.
Semenyo failed to directly contribute to a goal in that success, being guilty of profligacy in front of goal, but the 24-year-old has put up a respectable return of three goals and one assist in eight games so far.
Semenyo's eye-catching exploits this season are believed to have attracted the attention of both Arsenal and Tottenham, while Liverpool and Newcastle United have also shown an interest in the Cherries attacker.
Now, the former three clubs have all been handed encouragement that a deal for the Ghanaian could be struck in 2025, as Semenyo has confirmed that he is aspiring to play for a Champions League or Europa League team one day.
Semenyo: 'CL football will not come with click of fingers'
"Yeah, any team that plays Champions League, Europa (League) — that's the aim. I know that's not going to come with a click of my fingers, it's going to take some time," Semenyo told The Athletic.
"It's going to take goals. It's going to take a lot of consistent performances. But I've worked all my life for that and I'm just going to continue working hard. That's my mentality."
Semenyo - who arrived at the Vitality Stadium from Bristol City in the January 2023 window - also revealed that he has always supported Arsenal, and he realised a dream by playing against the Gunners.
"I am an Arsenal fan. I don't conflict the two with my job. It is great to play against Arsenal, a team I have watched all my life and I want to play for the top clubs as well. In order for that to happen I need to prove it," Semenyo added.
Bournemouth paid just £8.5m to bring Semenyo to the South Coast in January 2023, but the Cherries would certainly be well-placed to demand a higher fee for the 24-year-old next summer following his success this season.
Why Arsenal should go all out for Semenyo signing
Originally arriving at Bournemouth as a striker, the Ghanaian - who was born in London - has effectively transitioned to a right-wing role and now boasts 12 goals and three assists in 55 matches for the Cherries.
Semenyo may not force his way into the first XI over Bukayo Saka at Arsenal, but if Saturday's game showed anything, it is that the Gunners desperately need to find a reliable backup to the Englishman.
Reiss Nelson and Fabio Vieira have both played that role in recent times, but neither has shown that they can be long-term solutions, and they were sent out on loan this summer to Fulham and Porto respectively.
Nelson's Arsenal career in particular appears to be nearing its end, and it is unclear whether Vieira can reignite his Gunners career either; if he does, he may be better suited to the role of Martin Odegaard's deputy rather than Saka's.
As the latter is always going to draw fouls and pick up bumps and bruises, signing Semenyo for a reasonable fee is surely a no-brainer after his come-and-get-me plea.