Walcott, 23, is into the final season of his current contract but has yet to negotiate an extension, with the two parties said to be at an impasse over wages.
There had been suggestions the England forward - who could sign a lucrative pre-contract agreement with another club in January - would be offloaded in the last transfer window to avoid him moving as a free agent next summer, which Wenger refuted.
However, the Frenchman acknowledged the situation was reaching a make-or-break point with the player he signed from Southampton as a 16-year-old.
"I still hope to sign him and the next two months will be vital because after that, the longer this situation lasts, then the more difficult it is," Wenger said.
"Let's hope we can find a solution in the next two months."
Asked if Arsenal would consider selling Walcott during the January transfer window,
Wenger added: "It will depend on the needs of the team and the club.
"We can afford to go to the end (of the contract) if needed."
Walcott has not started a match since the opening day against Sunderland and received a mixed reception from some sections of the Emirates Stadium when coming on against former club Southampton on Saturday.
Wenger added: "The fact he doesn't play regularly at the moment is right, but it's not necessarily linked with his contract situation. No player is happy when he doesn't play.
"At the moment, [Laurent] Koscielny doesn't play. He has just extended his contract and still doesn't play because the defence is doing well.
"That's only temporary because by the end of the season they will all play."
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.