The 27-year-old, who joined Zenit from Genoa in 2011, has been reported as a target for a host of top-flight Italian sides including the likes of city rivals AC and Inter Milan.
Prior to his switch to Russia, Criscito had spent his entire career in Italy, including a brief spell with Juventus during the 2007/08 season.
Criscito is capped 22 times by his country and although he refuses to rule out a return in the future, he says he is content with Zenit, where he remains under contract until 2016.
"The rumours about the interest of AC Milan, Inter Milan, Roma and Napoli flatter me, but I'm fine in St. Petersburg and I have not asked to leave," he told calciomercato.it.
"The relationship with (Andre) Villas-Boas is great and I still have a two-year contract with the club. Sooner or later I want to come back to Italy, but now I'm only focused on Zenit."