Criscito has called St Petersburg home since 2011 but the Italy international is reportedly attracting the attention of Roma, with former Zenit boss Luciano Spalletti expected to replace Rudi Garcia, who was sacked on Wednesday.
Spalletti and Criscito worked together at Zenit until 2014 and combined to win the Russian Premier League and Super Cup in 2011-12.
Asked about his countryman and a potential return to Serie A, the former Genoa and Juventus left-back told SportItalia: "Spalletti is a fantastic person and I am happy he's getting back to work. People like him are good for football.
"He was an important coach in my career, he brought me to St Petersburg and we had a wonderful three years together.
"Will I go to Roma? I don't know. We'd have to see if the coach still wants me... I would be proud to receive a call from Roma.
"I do miss Italian football. I watch it from Russia. I should also note I am very happy here and nobody has called me so far.
"I am happy with the way my career has gone so far. I'd like to get back into the national team. We're approaching Euro 2016, so we'll see what happens."