The England international's current contract expires at the end of the season and Chelsea boss Rafael Benitez has already said that the player won't be offered a new deal.
Now, it is understood that Juventus are offering Lampard a way out of Stamford Bridge in the upcoming transfer window.
The 34-year-old is able to sign a pre-contract agreement with foreign sides in January, although the Turin club are keen on a cut-price deal instead, which would see Lampard join them straight away.
MLS clubs LA Galaxy and New York Red Bulls have also been linked with a move for Lampard. However, according to Corriere Dello Sport, Juventus are the favourites in the battle for the former West Ham United man's signature.
Lampard joined Chelsea in 2001 for £11m.