Gomis is one of the most sought-after free agents in the transfer market after seeing out his contract at Lyon.
The 28-year-old is being chased by a number of clubs across Europe, having scored over 100 goals in Ligue 1 during his career.
The likes of West Ham, Sunderland and Swansea are all thought to be admirers of Gomis and the player has been in England to talk to interested clubs this week.
Gomis' representative, Willie McKay, has confirmed he has spoken to five clubs about the striker and that one club in particular are making a concerted effort to land the France international.
"I am speaking to five Premier League clubs about Bafetimbi and it is no surprise there is a lot of interest in him as he is one of the best free agents out there," McKay told Sky Sports.
"I am speaking to one very ambitious chairman of an ambitious club and they are very keen to sign him and Bafetimbi will go to a club who proves they really want him.
"The club who are really pushing for him have held a long-term interest in him and made a big bid for him before when he was under contract at Lyon."