Walcott has so far failed to reach agreement with the club about a new contract and is set to become a free agent next summer unless a deal can be struck.
The winger provided a reminder of his value when he scored the opening goal in Arsenal’s 2-2 Champions League draw with Schalke earlier this week, taking his tally to eight goals for the season.
It was Walcott’s first start in the Premier League or Champions League for two months, and should guarantee his inclusion in the starting line-up against Martin Jol’s Fulham.
And Arsenal manager Wenger has made it clear he will do everything he can to keep the England international at the club.
He said: “My desire is to keep Theo. We do what’s needed to keep him and hopefully, (as) I told you many times, we can sort this situation out very soon.
“Very soon is before the end of December — one way or another, that is for sure. I don’t want to go into any details but you can believe me (that) we do the maximum we can to keep our best players.”
Wenger concedes that his side face a testing challenge against an in-form Fulham side, as they attempt to get their league campaign back on track.
An impressive start to the season has given way to an indifferent run that has threatened their progress in the Premier League and in Europe, and Wenger admits his side’s home form must improve.
He said: “We had one or two flat games at home, I agree. Especially the game against Schalke (a 2-0 loss), even the game against QPR (a 1-0 win).”
And warning of Fulham’s threat, he added: “Of course, they have scored 21 goals, they are very efficient going forward.
“They have (Hugo) Rodallega, they have of course (Dimitar) Berbatov, and offensively they are a side who creates many chances and who score goals. Twenty-one goals is quite impressive in 10 games.”
Alex Oxlade-Chamberlain and Aaron Ramsey face late fitness tests for the Gunners and Jack Wilshere will miss the game through suspension.
Arsenal are only ahead of Fulham on goal difference after 10 matches of the season, despite manager Jol losing several key players, like Clint Dempsey and Mousa Dembele to Tottenham Hotspur.
But despite Arsenal’s recent troubles, Jol does not think his side can finish above their London rivals.
“If they don’t do the same as they have in the past, then we could have a chance, but Arsenal are capable of being in the top four again,” he said.
“With their quality and resources, of course they should finish above us. It would be ridiculous if we (were above) a club like Arsenal.
“Wherever you are, every manager is under pressure, but he (Wenger) is one of the few who will never be under pressure. People realise what he has done, not only in the past but last year.”
Jol was Tottenham manager in the last north London derby at Highbury in April 2006.
Arsenal have still not won a trophy since moving to the Emirates, but the Dutchman says that times have changed.
He said: “They are in a different position now. If you look at Man City, with almost half a billion spent, Man United, Chelsea — it’s not easy.
“They do what a lot of other clubs do — they don’t spend all the money in the world but they are still capable of getting all these great talents.
“They will do very well to finish in the top four, but can you expect them to win things?”