The 23-year-old's current contract runs out at the end of the season and an agreement over a new deal has yet to be reached.
"I believe he is doing very well," Wenger told Arsenal's official website. "I haven't changed my mind on him.
"I always said I want to keep him and we [will] try to find an agreement. We haven't found it yet but we'll continue.
"He doesn't play like somebody who wants to go and I don't behave like somebody who wants him to go because he plays."
Walcott was on target in Arsenal's 5-2 victory over Tottenham Hotspur at the Emirates on Saturday.