The 35-year-old will be leaving Manchester United next month after both the club and interim boss Ralf Rangnick confirmed that his contract will not be renewed beyond this season.
According to Calciomercato, interest in Cavani is rife, with a number of Italian clubs, including Fiorentina, keeping a close eye on the veteran striker's situation.
The report adds that La Viola are yet to make contact with the player's representatives, and a potential move for the Uruguayan would depend on whether his salary demands would comply with the club's wage structure.
Fiorentina believe that Cavani would be tempted by a return to Italy, where he spent six years between 2007 and 2013 during spells with Palermo and Napoli.
Cavani made 20 appearances for Man United in the 2021-22 campaign, scoring only twice and registering just one assist.