The 26-year-old left Genoa for Russia in an €11 million move in June 2011 and has since made 66 appearances for the club, winning the Russian Premier League in his first season.
Criscito has spent the festive period in his homeland, and has been linked with an imminent move to Stadio Artemio Franchi, as well as previous clubs Juventus and Genoa.
The left-back's representative, Andrea D’Amico, told La Gazzetta dello Sport that the Italy international is fully open to making a move back to Serie A.
"We are ready to talk to Fiorentina without problems," he said.
Criscito has made nine league appearances for Zenit this season after recovering from a ruptured cruciate ligament.
He has also made a tentative return to the international scene after being dropped from Cesare Prandelli's squad for UEFA Euro 2012 amid allegations of match-fixing, which Criscito was cleared of any involvement in.
