Wenger was pressed about Van Persie by journalists after his side had lost 2-0 to Manchester City on the latest leg of their Far East tour.
City, Juventus and Manchester United have been linked with a move for player - and Wenger has become annoyed by the speculation.
"We have talked about Van Persie," he said.
"I have talked about Van Persie and I'm not talking about that question any more."
The Dutchman has missed Arsenal's tour and is instead working on his fitness following Euro 2012.
Wenger added: "Van Persie is close to fitness. But we have not had any more contact from City or United about him."
City manager Roberto Mancini backed up Wenger's claim that no bids had been made.
"If he said this, I think it's true. Van Persie is one of the best strikers so it's difficult to buy him," said Mancini.
Dutch defender Ron Vlaar has agreed terms on a three-year move to Aston Villa.
The 27-year-old centre-back will have a medical at Villa Park next week before completing the deal, which had looked to have collapsed last week.
Andy Carroll will only leave Liverpool for a new club if it can provide the England striker with European football.
The 23-year-old, who scored at Euro 2012 this summer, is keen to stay at Liverpool and prove himself to new manager Brendan Rodgers, but is coming to terms with the fact that he might not be required at Anfield.
But reports from England today suggest that the £35million (Dh200m) man is not prepared to move on anyone's terms but his own - and only to a club which is playing in Europe next season, seemingly ruling out a move to Upton Park.
Glasgow Rangers will be allowed to field a team at Brechin tomorrow - but Ally McCoist has hit out at Scottish football chiefs for leaving the side in limbo on the eve of the new season.
Sevco Scotland - the company set up after Rangers' collapse at the end of last term, have been granted conditional membership of the Scottish Football Association following two weeks of discussions but there remains disagreement between the SPL and the Rangers newco.
Sevco, who bought the assets of Rangers last month, accepted a delayed 12-month transfer ban handed to Rangers in April as well as about £3million in football debts.
But Ibrox manager Ally McCoist hit out at the SPL and Sevco board members vowed to challenge any SPL decision over the tax scheme, which could have left the old Rangers company with a £75million bill.
"Forty-eight hours from now, we are supposed to start the season with a game at Brechin and, as I sit here today, I don't know exactly what our status in the game is, where our players that we have should be registered - and what the future holds for us going into next week," he said.
"It's a ludicrous situation"