Walcott's protracted negotiations over a £100,000-a-week extension is not expected to be resolved in the immediate future, although Wenger says the 23-year-old will not leave the club during the January transfer window with his current deal set to expire in the summer.
The Arsenal manager hopes the new contracts agreed by Jack Wilshere, Kieran Gibbs, Alex Oxlade-Chamberlain, Carl Jenkinson and Aaron Ramsey will persuade Walcott to sign. Wenger also believes the club deserves a commitment after assisting the player's development.
"I am happy to pay Theo the money he deserves. You feel as well, I bought Theo at 17 years of age and spent a lot of money for him, gave him big support as well. I believe he's happy here, he's always looked to me like he's an Arsenal man," said Wenger, whose side drew Bayern Munch in Thursday's Champions League last 16 draw.
"You want the players to stay because they love where they are and they are committed to the club. That is the most important. What is important to keep the young players together is at some stage I stand up for them.
"When they are ready to produce you would like to say: 'OK let's stay together and win together, and give back to the club what the club has given to us.' My gut feeling is that he belongs to this club and I hope he will do it and sign for us. Once he has made up his mind it will be very quick."
Walcott, signed by Wenger from Southampton in 2006, has been holding out for an improved offer and could potentially sign a pre-contract agreement with other clubs in January if the current situation is not resolved.
Alisher Usmanov, the Russian oligarch who holds a 29% share in Arsenal, has criticised Wenger for making "a mistake" when deciding to sell Robin van Persie to Manchester United last summer. Wenger, though, defended his transfer policy and said his recommendations to the board for suitable wages and fees for players are usually accepted.
Asked if Walcott was worth a £100,000-a-week salary, he said: "I never see football like that, you never fix yourself a limit on financial restrictions or not. At the end of the day, can you pay what the players want and does it fit with your wage structure?
"I'm happy when the players make big money but it has to be made possible for the club to pay it. I believe the board will follow my recommendation if it is possible. We have a wage bill that has to be respected. When you go higher than expected I ask the board to do it and most of the time they follow my demands.
"Robin was 29 [when he left], Theo is 23. I believe it is important we keep him. I don't want to compare it but it would be a big loss for us. I want him to stay and I have been consistent on that."
Walcott will play for Arsenal against Wigan Athletic at the DW Stadium on Saturday. Wenger has no fresh injury concerns following the 5-2 victory at Reading on Monday night.
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