Multiple sources have confirmed that the Viola are giving some thought to a massive offer from Premier League side Leicester for the Argentina international in the January transfer window.
Sportitalia now claim that if Gonzalez is sold, then Fiorentina have already set their sights on his potential heir in the starting XI.
It would be 26-year-old French left-sided attacking winger Bamba, who will be out of contract with Lille at the end of this season.
Because of his situation as an imminent free agent, Bamba has already been linked with a potential proposal from Serie A leaders Napoli, but Fiorentina would guarantee more regular playing time.
So far this season, Bamba has scored four goals and provided three assists in 16 Ligue 1 appearances for LOSC.