Van Persie, 28, has yet to agree a contract extension, which runs until the summer of 2013.
Manchester City manager Roberto Mancini has fuelled speculation of another big-money raid on Emirates Stadium for the Holland striker, whom he hailed as "one of the best strikers in Europe".
Over the past few years Wenger has seen Emmanuel Adebayor, Kolo Toure, Gael Clichy and Samir Nasri, last summer, all join title rivals City in big-money moves.
Van Persie has netted 32 goals in a stand-out individual campaign and appears comfortable to wait until the end of the season before discussing future plans.
Wenger has already stated the club will "do anything possible" to retain the services of their talisman striker, and sees no reason to let City's public courtship of Van Persie unsettle either the player or his team.
"We will not lose anybody to Manchester City, or to anybody else because we want to keep our players," the Gunners boss said.
"We want to keep Robin Van Persie, that is clear, we will do everything possible to extend his contract, that is clear, and apart from that, I can only let people talk."
Wenger insists everyone's focus must be on winning Monday night's Barclays Premier League clash with Newcastle to stay in the top four.
"To fulfil his contract is to win against Newcastle and to add to that is to win the next game, that is being professional," the Arsenal boss said.
"You always want to know what happens in 2012 or 2013 then who knows? To be professional is to win your next game."
Arsenal reluctantly sold then captain Cesc Fabregas back to Barcelona last summer, before eventually having to give up in the battle to keep Nasri, who was sold in a £24million deal at the end of August.
Wenger admits it is a situation he does not want to repeat.
"Last year was the first time we lost the players young. That was a worrying sign and it provoked double trouble," he said.
"Firstly they went late and secondly we bought late when we were already in a very difficult situation.
"There is a wrong understanding about what happened. The club has been treated very badly because of that and I don't think the club was guilty of anything during that transfer period."
Wenger continued: "I was very adamant [Nasri would not be sold], but at the end of the day, it was a difficult situation to manage.
"We had the players and we felt after the tour, that [Aaron] Ramsey and [Jack] Wilshere could work, also we could add somebody more.
"If a player didn't want to extend, where do we go from there? But we will see. We do our best to keep our best players."
Reports in Germany have suggested Arsenal are set to sign Lukas Podolski from Cologne for £11million.
Wenger insisted no deal had yet been done for the Poland-born 26-year-old, who has played at two World Cups.
"He is a good football player above all. He can play for us because he can play central, he can play right and he can play on the left," Wenger said.
"He has 96 caps for Germany and is 26 years old which is the best age.
"He is available at a reasonable price if we can reach an agreement, but at the moment we are nowhere near.
"I don't want to disappoint people and let down their expectations.
"Let us first see what we can do."