Walcott's future has been surrounded by speculation after the former Southampton man claimed that he wanted to be played as a central striker rather than out wide.
Wenger, however, has talked up his player's ability as a striker after his hat-trick against Reading in the League Cup, and admitted that he would like the 23-year-old to stay with the Gunners.
"He has the qualities to play as a striker and I hope he will be a striker at Arsenal," said Wenger.
"I always said I want to keep him. During the contract talks you have to give him credit for the way he's committed to the team and the way he behaves."
Arsenal were drawn away to Bradford City in the League Cup quarter-finals.