Rotherham are unlikely to make any more signings before the end of the month, according to manager Steve Evans.
Derby captain Richard Keogh has agreed a new three-year contract with the Sky Bet Championship outfit.
The England forward is currently in negotiations over an extension to his deal which expires in the summer.
Wenger is adamant that Walcott will not be sold in January, but as yet there are no signs of a swift conclusion.
Walcott is said to be determined to prove himself in the central striker's role, from where he scored the final goal in a 5-2 win at Reading on Monday night, 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.
"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," Wenger said.
"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.'
"Somewhere along the line they need to give back to the club what the club has given to them.
"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."
Wenger is expecting to take a similar squad to Wigan on Saturday as he fielded at Reading, where Walcott was preferred over Olivier Giroud in attack.
The lunchtime clash against the Latics is Arsenal's last until a home game with Newcastle on December 29 after the Boxing Day fixture with West Ham at the Emirates Stadium was postponed because of industrial action by some London Underground staff.
In the new year, Arsenal will resume their Champions League campaign against Bayern Munich after been paired with last season's beaten finalists in this morning's draw.
Bayern are nine points clear at the top of the Bundesliga but German striker Lukas Podolski sees no reason why Arsenal should not be able to knock out his old club.
Podolski, who spent three seasons at Munich from 2006, said: "It is a big club, but we have the chance to win."