Reports have suggested long-term admirers Juventus are preparing a new approach for the forward amid speculation of a breakdown in contract talks at Emirates Stadium.
Walcott's current deal expires in the summer of 2013 and he is rumoured to be demanding a significant pay rise in order to stay at Arsenal.
But Wenger, who had to sell Cesc Fabregas and Samir Nasri in 2011 amid a contract standoff, has rubbished the conjecture about the 22-year-old.
The Arsenal manager is quoted as saying: "We want to keep Theo and he knows that. Of course (he earns his money) he works every day and works very hard.
"His attitude is great, I have no problems with that at all."