Montpellier coach Jean Fernandez has resigned after overseeing a run of seven Ligue 1 games without victory.
Liverpool goalkeeper Pepe Reina would welcome a return to Barcelona next summer.
Both players have been granted permission by the Florence-based club to undergo a medical with Napoli before completing permanent transfers to the azzurri outfit.
A statement from Fiorentina read: "After the negotiations undertaken by ACF Fiorentina and SCC Napoli, our players Valon Behrami and Alessandro Gamberini have been authorised to undergo medicals with Napoli."
Behrami, a Swiss midfielder, joined Fiorentina in 2005 from Bologna.
The 27-year-old is set to sign a three-year deal with the Partenopei side.
Italian central defender Gamberini, meanwhile, is expected to put pen to paper on a contract that will keep him tied to Napoli until June 2016.