The Sun says Berba's contract runs out next summer and the Spaniards hope to land him in a cut-price £12million deal.
Berbatov, 30, is United's top scorer but is now playing second fiddle to Javier Hernandez.
Seville have sounded out the Bulgarian's agent Emile Dantchev but any deal depends if United will take such a cut after paying Spurs £30.75m for him in 2008.
Berbatov has hit 48 goals in 123 games - including 22 and three hat-tricks this season - but fans have never warmed to him.
Hernandez is seen as the better option alongside Wayne Rooney.