The Italy international's agent 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 linked with the big teams I enjoy it," Criscito told La Gazzetta dello Sport. "My agent has spoken with Milan and is working on things with Zenit. I would take a pay cut to join Milan.
"Milan have been after me for some time and this can only make me happy, now we are having contact 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 prestige, as in Russia I'm fine, my family is settled and every year I play in 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.