The Egyptian spent the second-half of the season on loan at the Serie A club and caught the eye with a series of top displays.
Fiorentina are in pole position to land the player for the 2015-16 campaign, with an option to extend his loan in place.
However, they could now face a battle for his signature, with Atletico Madrid and Tottenham Hotspur eyeing the player.
Reports in Italy suggest the duo are keen on the winger as they assess their options this summer.
Corriere dello Sport also claims Atletico have made contact with Chelsea directly over a deal for Salah.
