The Bundesliga club are reportedly keen to rival Villa for the Manchester United loanee when he becomes a free agent this summer.
Cleverley, 25, has been in resurgent form since Tim Sherwood’s appointed as Villa manager, scoring in three consecutive games to help edge the club towards Premier League survival, while also earning support for an England recall.
Former boss Paul Lambert could have signed the United-owned midfielder in the winter for £7.5 million but failed to exercise their purchase option due to the poor performances which saw him become a target for abuse from a large section of fans.
He has since managed to win over their support with his recent showings, though, and, with his United contract expiring on June 30, Sherwood has not hidden his desire to re-sign the soon-to-be free agent to a long-term deal.
However, Wolfsburg, who are on course for a second-place finish in the Bundesliga and Champions League football, are now said to be keen on a move for the in-form Villa man, with Everton and Arsenal also named as interested parties.
According to Sky Sports, Cleverley’s international future will be a big factor in deciding his next move, as the Old Trafford product is desperate to get back into the England picture after a 15-month absence.
The 13-times capped midfielder seems to think that Villa Park could be the place where he can achieve that, though, having suggested after the weekend’s 1-0 win over West Ham United that he is eager to sign on the dotted line for the claret and blues.
“I’m playing my football with a massive smile on my face and enjoying myself here,” he told the Birmingham Mail. “I’ve really grown to like playing for this club in the last few months and this manager has got to be given credit for getting me where I’ve been in the last few weeks.
“First of all you’ve got to be playing in a position where you fit in, and playing at a club where you like the players and the manager. This club ticks all the boxes so we’ll see what happens.
“I don’t think any Premier League players are going to be short of a quid or two so I think you’ve just got to be happy first and foremost and I am at this club so let’s just see where we go from there.”
With those comments in mind, if Cleverley's ultimate decision comes down to weighing his happiness against the lure of Champions League football, it sounds like he might well choose the former and commit his long-term future to the Tim Sherwood-led revolution at Villa.