The San Siro side have shown an interest in luring the Italy international back to Serie A after a spell in Russia
The San Siro side are keen to strengthen their squad after a disappointing 2013-14 campaign and they are confident Criscito would prove to be a fine addition to their defence.
The left-back started his professional career with Genoa and also enjoyed a spell with Juventus before leaving Serie A for Zenit St Petersburg in June 2011.
Criscito is keen to return to his native country, however, and a transfer to Milan could be on the cards this summer.
"There has been some initial contact, but it's too soon to say that negotiations are in the closing stages," D'Amico told Sportitalia.
"I can confirm that Milan like Domenico, though."
The 27-year-old has a contract with Zenit until the summer of 2016.