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."
Fabregas was also Gunners skipper when he moved away, returning to boyhood club Barcelona in a £30million deal during August 2011.
Wenger, however, feels the circumstances behind the transfer were understandable given the Spain international's strong ties to the Nou Camp, but maintains he can see a time when the 25-year-old could be back with the Gunners.
"Fabregas was an exception and I would try again (to sign him). For me he is a world-class player which you do not find. I am not convinced he will not come back here one day," Wenger said.
"In the next two or three years, certainly not because he is contracted with Barcelona, but maybe later.
"Cesc is really an Arsenal man, he loves Arsenal and watches every game, but of course Barcelona was where he grew up, so you have to accept that will come in (to the move), especially when Barcelona have the best team in the world."
Fabregas' former boss Pep Guardiola continues to be linked with taking over at Chelsea, who are said to be ready to shell out £54million to tempt him out of retirement.
Wenger believes the 41-year-old would be a good fit for Roman Abramovich's club, should the Russian decide to dispense with interim manager Rafa Benitez.
"Guardiola started his career with caviar - will he get caviar at Chelsea? Certainly yes as well, it is a good ingredient also to do well. It depends on the quality of the players," said the Arsenal boss.
"He is a great manager, but at the moment Benitez is there and he is a great manager as well."
City will be out to avoid falling further behind leaders Manchester United tomorrow, but have not won a league game at Arsenal since 1975.
Defeat for either side would severely dent their ambitions, as the Gunners are looking to keep within striking distance of the top four.
Wenger said: "Is it (title race) over? You don't know, but it is a game you don't want to lose, or even draw, you want to win."
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