Van Persie's future has been the focus of intense scrutiny for weeks since telling Arsenal that he would not be renewing his contract with the Londoners.
Speaking in Beijing after seeing his side lose 2-0 to City in a pre-season friendly, Wenger said: "At the moment I must say that the van Persie case has not crossed too much my mind.
"We have no offers, so he is our player. That is it. And for the rest, I do not think that there is any more need to talk about it."
Asked to confirm that he had not received a single bid for the striker, 28, he replied: "I have just told you."
Arsenal are thought to be demanding in the region of 20 million pounds for the prolific Dutchman.
The van Persie saga comes after Wenger lost key players over the last two seasons -- Samir Nasri to City and Cesc Fabregas to Barcelona.
City boss Roberto Mancini -- who is believed to be exasperated at the slow progress his club has made in luring van Persie -- was asked to respond to Wenger's claim.
Mancini said: "I think that if Wenger said that, then that is true.
"That is difficult because van Persie is the top top striker. One of the best strikers in the world. It is not easy to buy him."
Asked if City had made an offer, he said: "No, I don't think so."
Goals just before half-time from Pablo Zabaleta and Yaya Toure sealed victory for Mancini's men.
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