"Fiorentina have agreed personal terms with Dimitar and they'll announce the deal very soon," the source, who asked not to be identified, said, adding the transfer was subject to Berbatov passing a medical.
Berbatov, who became United's most expensive player when he joined from Tottenham Hotspur in 2008 for £30.75 illionm, had reached an agreement with the Serie A club on a two-year contract with an option for a further year.
The 31-year-old was the Premier League joint-top scorer in the 2010/11 season with 20 goals but has struggled to hold down a place in Sir Alex Ferguson's starting line-up since and was keen to revive his career in another top European league.
Ferguson made it clear it was probably time for Berbatov, who is Bulgaria's all-time leading scorer with 48 goals, to look for a move when he signed Dutch striker Robin Van Persie from Arsenal prior to the start of the Premier League season.
If the deal is completed, Berbatov will become the fourth Bulgarian in Serie A after defender Nikolay Iliev and strikers Hristo Stoichkov and Valeri Bojinov, who played for Fiorentina between 2005 and 2007.
Football experts in Bulgaria believe the transfer could also lead to Berbatov ending his self-imposed international exile.
Earlier this year, Berbatov, who quit the national team in 2010, said he would be open to an approach from coach Luboslav Penev after he moved to a club where he could play regularly.
