Respected journalist Gianluca DiMarzio claims the club has made initial contact with the Premier League legend.
Last week, Vardy was linked to a move to Celtic, with reports saying he was keen on joining the Bhoys.
Read more:
Cremonese secured promotion to the Italian top flight after defeating Spezia 3-2 in the play-offs at the end of last season.
Last week, Celtic manager Brendan Rodgers commented on the links with Vardy, saying: "Listen, I will not speak about any individual player.
"Of course, I worked really well with Jamie; he was brilliant for me in my time at Leicester.
"But no, there have been so many names floated about, but I wouldn't disclose either way."
Before the second leg of his team's crucial Champions League play-off with Kairat Almaty, he said: "I think by the time we get back, hopefully we’ll be close to one or two things."
Celtic are reportedly set to seal deals for Boca Juniors left-back Marcelo Saracchi and Michel-Ange Balikwisha of Royal Antwerp.