Wenger believes Wilshere will sign new Arsenal deal
Wilshere's contract is due to expire in June, which has prompted speculation he could be set to leave Emirates Stadium for nothing as he seeks regular playing time.
The 25-year-old spent the previous season on loan at Bournemouth, and had not started a Premier League game for the Gunners since May 2016, prior to forcing his way into the XI for each of the team's last three league outings.
Wilshere will hope to make it four starts in succession when Arsenal visit Crystal Palace on Thursday and Wenger confirmed talks are due to be held in the near future.
"I will sit down with him, yes," he told a media conference.
"I believe that, if we can meet a point of agreement financially, he will want to stay."
The manager discussed @JackWilshere in his press conference this morning
Check out what he said
https://t.co/QGDYlRuGdM pic.twitter.com/7exKOHK7Zo
— Arsenal FC (@Arsenal) December 27, 2017
While Wilshere's rehabilitation continues, Olivier Giroud has become a peripheral figure since Alexandre Lacazette's arrival, prompting reports of a potential move to Everton.
Toffees boss Sam Allardyce has suggested the French striker's wife put a stop to that switch, claims rejected by Wenger.
"No, I don't think so, because he could have joined Everton and stayed basically in London," Wenger said.
"I don't think that was the problem."
Giroud is out of action due to a hamstring injury, with Wenger expecting his compatriot to return in mid-January.
Nacho Monreal (ankle) and Aaron Ramsey (hamstring) are also sidelined, with the pair likely to be back in contention early in 2018.