The deal is thought to be for around £4m, four years after he joined the Red Devils for a club record fee of £30.75m from Tottenham Hotspur.
Berbatov is believed to have signed a two-year deal, with the option of a third.
The Bulgarian striker was joint-top scorer in the Premier League during the 2010-11 season with 20 goals, but has since fallen behind the likes of Wayne Rooney, Javier Hernandez and Danny Welbeck in the Old Trafford pecking order.
Neither side has officially confirmed the move yet, but the 31-year-old is known to have flown out to Florence to undergo a medical at the Serie A club.
Berbatov scored 56 goals in 149 matches during his time at United, winning two league titles, a league cup and a FIFA Club World Cup in the process.