The French club have previously indicated that they would be prepared to let Gomis leave, although Shakhtar Donetsk have dropped their interest after initially appearing to be favourites.
Swansea City and Cardiff City have also been linked with moves to bring the 27-year-old to the Premier League, while Fiorentina are the latest club to reportedly enter the race.
It is rumoured that Fiorentina have made an offer and are on the verge of agreeing a deal with Lyon's president.
Gomis said: "I will very soon be in Lyon to sort out my future.
"Lyon does not want to keep me but I will find a new home like I did when I left St Etienne."