The Italy international is desperate to return to his native country and has made it clear that he is willing to lower his demands to make a move happen
The Italy international's agent already claimed earlier this week that the Serie A side had contacted him over a potential transfer and Criscito is desperate to return to his native country after a three-year spell in Russia.
"When my name is combined with the big teams I enjoy it. My agent has spoken with Milan and is working on things with Zenit. I would take a pay-cut to join Milan," Criscito was quoted as saying by La Gazzetta dello Sport.
"Milan have been after me for some time and this can only make me happy, now we are having contacts with Milan, but I do not know at what point negotiations are.
"Milan remains one of the largest clubs in the world, with [Filippo] Inzaghi as coach the team will have more 'oomph', just as he had as a player.
"I would return to Italy only for a team of great coat of arms, as in Russia I'm fine and my family is well established, every year I play the Champions League, but I miss Italy and want to go back."
The 27-year-old Criscito has a contract with Zenit until June 2016.