Van Persie is understood to have sought assurances from Wenger this summer that the club's future was still bright following the sales of Fabregas and Samir Nasri, who refused to extend his contract and was sold to Manchester City.
Wenger understands why Van Persie was worried about the club's direction.
"If you're in Robin's place and you see Nasri going, Fabregas going, then you can be worried of course," Wenger said.
The club could be faced with a similar problem to the Nasri one if Van Persie does not sign an extension to his current contract, which expires in 2013, but Wenger is not concerned.
"Now he (Van Persie) is out? No, I don't think that really. Robin is not from Barcelona," Wenger quipped.