The England forward is currently in negotiations over an extension to his deal which expires in the summer. Walcott is said to be determined to prove himself in the central striker's role, while his representatives are also pushing for a package of up to £100,000 a week.
However, after taking a "gamble" on signing Walcott as a raw 16-year-old in a £12million deal in January 2006 and helping develop him into an England regular, Wenger feels Arsenal are owed a debt of gratitude, saying: "Somewhere along the line they need to give back to the club what the club has given to them."
The Frenchman added: "What is important to keep the young players together is that at some stage I have stood up for them; I played you at 17, 18, 19 years of age and I know I took a gamble.
"It is easier to take a player of 25 and put him in the team. You know what you are getting.
"If you put them in at 17 or 18, you have to stand up for them. You risk losing games while they are learning their job. Once you have produced them you want to say, 'Okay, let's stay together and win together.'
"When a guy gets to 30, you can understand it is his last contract and if he feels he wants a change. This is a more sensitive age, but basically, it is a reward for our policy."
Arsenal announced new long-term deals for British quintet Jack Wilshere, Carl Jenkinson, Aaron Ramsey, Kieran Gibbs and Alex Oxlade-Chamberlain on Wednesday, and it is hoped Walcott will be the next to sign on the dotted line.
Wenger says the Arsenal board could be prepared to stretch their wage structure in a bid to thrash out a deal, but insisted the club would not be held to ransom.
He added: "I am happy to pay Theo the money he deserves, but I feel as well that I bought him at 16 years of age and spent a lot of money on him. I am a big supporter and I believe he is happy here. Theo has always looked to me like he is an Arsenal man."
Source: PA
Source: PA