The 23-year-old has emerged as a target for a number of clubs, with both Villa and Celtic understood to be keen on landing him from Polish club Lech Poznan.
Tonev played in Lech's final game of the season on Sunday, and the club stated on their website that it was '99.9 per cent certain' that he had played his final game for them.
Werder have admitted that their interest in the 23-year-old, but they also state that there are a number of clubs looking to land Tonev.
General manager Thomas Eichin confirmed to Kreiszeitung Syke: "Aleksandar Tonev is with Lech Poznan. It's true we we would be happy if we could bring him over to our club (this summer).
"But, of course, there are different other clubs hoping to also secure his services."
Tonev has two years left on his current contract, with Lech believed to be asking around £3.5million for their star turn.
Reports in Bulgaria claim that Aston Villa legend Stiliyan Petrov, now on the coaching staff, has recommended Tonev to his bosses.