Although the sum is said to have fallen well short of Wenger's estimation - believed to be around £30million - United revealing their interest could further unsettle Van Persie, who has also been linked with Manchester City and Serie A outfit Juventus.
His existing deal at Emirates Stadium expires next summer and Wenger is desperate for the 28-year-old to remain a Gunner.
Van Persie won both Professional Footballers' Association and Football Writers' Association player of the year prizes in recognition of his phenomenal 37-goal contribution for Arsenal in the 2011/12 campaign.
The Dutch striker will not travel to Asia on Arsenal's pre-season tour, although the club were keen to stress his non-involvement was due to the striker having only trained for four days since returning from holiday. Other Euro 2012 players Per Mertesacker, Lukas Podolski, Olivier Giroud and Laurent Koscielny are also missing the tour.
The saga is shaping up to be a carbon copy of those that saw Cesc Fabregas and Samir Nasri both sold last summer – something which dragged on towards the tail end of the transfer window.
But Wenger is convinced that Van Persie will continue to give his all for Arsenal – regardless of whether he leaves the club.
"Robin was an exceptional leader last year," he said. "But we know how much we had to fight to come third because we missed out the start of the season. After seven games we had lost four and we have learned that for us it is vital for us to focus on the start of the season rather than on any transfers.
"If the transfers happen, they happen. As long as you are at the club you give your best for the club and that is the only pride you can have as a football player and as a manager.
"As long as you are somewhere you give your best every day for that club. If it changes, it changes. I am convinced that Robin is like that, he is completely focused every day on his job. He loves football, he loves the game and as long as he is here he will do that."
Arsenal have already signed two new strikers in Podolski and Giroud but are also said to be lining up Spain star Fernando Llorente should Van Persie leave.