The source told AFP that former Premier League winner Vardy will arrive in Milan on Sunday evening ahead of completing a one-season deal with an option for another should Cremonese stay in Italy's top flight.
Cremonese are on a perfect six points from their first two fixtures of the new Serie A season after beating Sassuolo 3-2 on Friday and winning against AC Milan at the San Siro last weekend.
Vardy left Leicester City after 13 years at the end of last season, bringing down the curtain on a relationship which created one of the most romantic stories in recent football history.
The 38-year-old signed for Leicester from non-league club Fleetwood town while in his mid-20s, having previously combined playing with a job as a factory worker.
He quickly made an impact in England's second-tier Championship, which he helped Leicester win in 2014 before becoming the goalscoring hero in their stunning Premier League triumph two years later.
During that title-winning season he broke a record previously set by Manchester United icon Ruud van Nistelrooy by scoring in 11 consecutive Premier League matches, and he won the Golden Boot for top scorer in the 2019-20 campaign.
Vardy, who netted 200 times in 500 Leicester appearances, also won the FA Cup in 2021 and earned 26 England caps, scoring seven times for his country.