The manager was frustrated by the repeated enquiries about the Dutchman's future in his post-match press conference following the pre-season defeat to Manchester City on Friday
Goal.com exclusively revealed last week that Van Persie would try to force a move to Manchester City by refusing to travel for Arsenal's tour of Asia but that the champions would take their time before launching any formal bid.
Sir Alex Ferguson admitted Manchester United's interest in the player, but signing the Dutchman is not currently a priority at Old Trafford.
Gunners officials claim that Van Persie is at the club's Colney training base as he looks to build up his fitness but, after he declared that he would not be signing a new deal, his future at the Emirates Stadium looks bleak.
When journalists quizzed Wenger on the subject, though, the Frenchman was in no mood to discuss his striker's future and instead concentrated on his side's performance in the wet conditions of China's Bird's Nest stadium.
"The Van Persie case doesn’t cross my mind," Wenger told the assembled press. "We have had no offers. He is close to fitness, of course, but we have not had any contact about him at all.
"We will not come back forever on Van Persie, We have many strikers at home. Van Persie is one of them, but we also have [Lukas] Podolski and [Olivier] Giroud.
"For now, we must prepare for the season and it is about more than one player."
When it was posed to Wenger that various sources had reported the bids from City, United and Italian giants Juventus, however, he grew riled at the interrogation regarding his captain.
"We have talked about Van Persie," he fumed. "We have just played a football game tonight, there are four English people here and there have been four questions about Van Persie.
"I have talked about that, I am not talking about that question anymore. Do you understand?
"If you understand and respect what I said, then why do you ask me again?"
It had been widely reported that, along with United, City had submitted an initial offer for Van Persie but the manager of the defending Premier League champions, Roberto Mancini, backed up Wenger's comments.
"No, I don’t think [we have made an offer]," said the Italian. "I think it is like this.
"If Wenger said this, I think it is true. Van Persie is one of the best strikers in the world, so it is difficult to buy him."