Walcott has been linked with a move away from the Emirates Stadium, with Liverpool among the clubs said to be interested in the England international.
The 26-year-old last month rubbished talk of a bust-up with Wenger, but stated he had not yet entered negotations over a new deal with just over a year remaining on his current contract.
Arsenal manager Wenger on Thursday tipped Walcott to get back to his best after a frustrating season, during which he returned from a serious knee injury, and is eager for the former Southampton man to extend his stay at the London club.
He told reporters: "I believe he will have a great future and I want him to stay here.
"Walcott is getting better every week and will have a great goalscoring record in the future."
Wenger also revealed Wojciech Szczesny will start Saturday's FA Cup semi-final against Reading, but Mikel Arteta (ankle) and Alex Oxlade-Chamberlain (groin) remain sidelined due to injury.
