The 23-year-old’s future has been a source of constant speculation in recent months, with the forward’s current contract set to expire in the summer.
Walcott is understood to have agreed a deal in the region of £90,000-a-week over the last few days but is yet to put pen to paper.
And Wenger, whose side host Manchester City on Sunday, believes tying the England international down to a new deal is key.
“Theo signing would at least give a positive message out for us,” said Wenger. “To the fans who love the club, that the way is not necessarily the exit but stability.
“When you go for a policy of young players like we have, you know when they get to 23-30 or more they will play for you, but if you give them a chance at 18 and at 23 they leave, you have basically worked for another club.
“[Alex] Chamberlain is 19, [Jack] Wilshere is 21, Walcott is 23, [Carl] Jenkinson 20, [Kieran] Gibbs 23. You need this core inside which represents the strengths and values of a club. We had that before – [Thierry] Henry and [Patrick] Vieira stayed for eight or nine years – and we have created it again.”
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