Manchester United boss Sir Alex Ferguson revealed on Friday his side tabled a bid to bring the Dutch striker to Old Trafford.
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.
"For me, Van Persie is one of the best strikers in the world, if not the best, and my desire is to keep him at the club." he told Arsenal Player.
"As for the rest I will do what is in the best interests of Arsenal Football Club. That, at the moment, is where we are. There is not a lot more to say than that."
Van Persie won both Professional Footballers' Association and Football Writers' Association player of the year prizes in recognition of his phenomenal 36-goal contribution for Arsenal in the 2011/12 campaign.
Press Association Sport has learned he will not travel to Asia on Arsenal's pre-season tour, although the Gunners were keen to stress his non-involvement was due to the striker having only trained for four days since returning from holiday.
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 Lukas Podolski and Olivier Giroud but are also said to be lining up Spain star Fernando Llorente were Van Persie to leave.
Wenger was also quick to defend the direction the club is headed in.
"We always defend the values of the club, and the model has to be self-sustainable, otherwise it can completely go out of shape and become very fragile," the Frenchman said.
"The financial solidity of the club is vital, for me, and therefore I have always supported that and I will continue to do that.
"I believe that the Financial Fair Play is about that. If UEFA push it through they will have a big supporter in me.
"I believe that football has to work like every single company, it has to work with the money it produces itself."
Wenger, who saw Cesc Fabregas and Samir Nasri leave last summer, added: "We are now 15 years on the trot in the Champions League and I believe that shows that our model works.
"On the other hand we are very ambitious, we want as well to win trophies.
"It's not enough just to be in the Champions League and we are focused on that of course.
"We work very hard to make the team stronger. In this job, when you have consistency in your attitude you can stay at a certain level.
"The most difficult thing is to be consistent and we have shown over the last 15 years that we can maintain that consistency.
"I am confident that we have to be faithful to what we believe is right in football and in the game - the way we play football."