Sky Sports sources understand the Bulgarian has flown to Germany for a meeting with representatives of the club he left in 2006 to join Tottenham.
There is also believed to be interest from Leverkusen's Bundesliga rivals Bayern Munich and Russian side Anzhi Makhachkala.
Berbatov, who joined United for £30.75m from Spurs in 2008, has slipped down the pecking order and, with his current contract set to expire in the summer, he has been linked with a move away from Old Trafford.
The 30-year-old said last month he had no plans to leave, but he was spotted on Sunday taking a flight to Frankfurt, where he was expected to hold discussions with Leverkusen.
Despite finishing as the Premier League's joint-top scorer with 22 goals last season, Berbatov has dropped to fourth choice striker behind Wayne Rooney, Danny Welbeck and Javier Hernandez.