Arsenal are determined to complete negotiations with Walcott's representatives over a contract extension, which is reported to be worth around £90,000-a-week.
Last summer, Wenger was unable to convince then captain Robin van Persie to stay on, as the Holland striker followed the likes of Cesc Fabregas, Samir Nasri and Emmanuel Adebayor in continuing their careers elsewhere, joining rivals Manchester United in a £24million move.
However, Wenger feels should a deal for Walcott be pushed through, it would send a message of intent that the likes of fellow England youngsters Jack Wilshere, Alex Oxlade-Chamberlain, Carl Jenkinson and Kieran Gibbs are all here to stay.
"Theo signing would at least give a positive message out for us, to the our fans who love the club, that the way is not necessarily exit, but is stability. We are not there yet (with Walcott), but I hope we will get there," said Wenger, whose side host Manchester City on Sunday.
"When you go for a policy like we have for young players, you know when they get to 23 to 30 or more, they will play for you - but if you give them a chance at 18 and then at 23 they go somewhere else, you have basically worked for another club.
"What we want is the players to grow up together and say they will be successful together.
"Chamberlain is 19, Wilshere is 21, Walcott is 23, Jenkinson 20, Gibbs 23 - they are all good players.
"You need a core inside which represents the strengths and values of the club.
"We had that before - [Thierry] Henry, [Patrick] Vieira, they stayed eight or nine years all together - and now we have created that again."