The central midfielder's future at the Emirates Stadium looked uncertain six months ago, having only started four Premier League games for the Gunners since October 2014.
But Wilshere has played 90 minutes in the last four league games for Arsenal and the 25-year-old says he's confident a new contract can be agreed before his current one expires in June 2018.
Wenger shares his optimism and revealed the club will "sit down" with Wilshere once the busy festive fixture list has passed by.
"We need to sit down with [Jack]. Beginning of January, it's planned," the Arsenal manager told reporters.
"There is no delay. I said we would sort out his situation in December, end of December. I told him we want to meet and sit down with him to talk about the future. That's what I did.
Wilshere is one of a few star players who is at risk of being poached in 2018 due to his contract running down, with fellow midfielder Mesut Ozil and forward Alexis Sanchez also set to be available.
Wenger does not believe their unresolved long-term futures does not affect them putting in shifts for him at Arsenal, as shown with Alexis' two goals and Shkodran Mustafi's opener ensured all three points at Selhurst Park.
"We are focused on short-term, that means the next game with the players committed and ready to fight," Wenger added. "It's not a guarantee of how long you stay somewhere. As long as you are somewhere, you give your best.
"They are questioned, always, when people don't have long contracts. The best way to show they are committed is to give that kind of performance.
"Jack is coming back in competitive shape. He gives something to the team, and gave a good final ball for the third goal.
"At 3-2 it became nervy again, and it finished in a less controlled way, but it was a good team performance."