The 24-year-old midfielder joined Lyon last season and he was loaned out to Lorient in the January transfer window.
Faivre has made 14 league appearances for Lorient so far, contributing three goals and three assists in the process.
His performances in the second half of the season have now sparked interest from Premier League clubs.
Fulham and Bournemouth are both keen on Faivre’s signature and it has been suggested that Lyon are willing to sell the player in the summer.
According to French outlet Foot Mercato, Fulham and Bournemouth have both held discussions with Favire’s entourage.
Bournemouth, who are owners of a 40 per cent stake in Favire’s current club, Lorient, want to sign the player in the summer with the possibility of loaning him back to the French outfit.
Fulham want strengthen their team for next season following an encouraging campaign under Marco Silva.
Lyon want €15m for the midfielder and it remains to be seen which of the two clubs will be able to convince Favire to join them in the summer.
