The 34-year-old looks set to leave the Premier League giants this summer with his current contract due to expire.
Despite his status as a senior member of the Blues’ squad, the club are unwilling to offer him a new contract as they look to lower their wage bill and usher in a new generation of players.
Lampard’s agent recently revealed that his client would be open to playing in Italy amid rumoured interest from Lazio.
Since these comments, both Fiorentina and Juventus have upped their interest in the goal scoring midfielder.
The Florence-based team are thought to be extremely keen, with club president Mario Cognigni hinting that the England international is just the sort of player they are looking to sign:
“Lampard is a player I have always liked and may be an example of today’s marketplace.
“A player who has passed 30 years, his contract is expiring, and he may be the right combination between experience and cost of the deal.”
Lampard is free to discuss a pre-contract deal with foreign teams due to there being only six months remaining on his contract.
This has opened the door for Fiorentina, who could offer him a lucrative contract as they will not have to pay a fee to Chelsea.
They may face competition from a number of teams from the Chinese Super League and MLS who are keen to utilise the player’s global image.