The 20-year-old has just returned from a long injury lay-off and is understood to be in preliminary negotiations over a contract extension.
Wenger believes along with fellow England internationals Kieran Gibbs and Alex Oxlade-Chamberlain, Wilshere - who has been at the club since the age of nine - can become the heartbeat of the team.
"He has two-and-a-half years left - that's quite a long time. We have built a team [where] we have a lot of young English players, or British players like Gibbs, Chamberlain, Wilshere. We still have the case of [Theo] Walcott, Aaron Ramsey. You want them all on long-term contracts," Wenger said.
Walcott, meanwhile, has yet to commit himself past the end of the season, with Wenger today revealing "unfortunately, I cannot give you any news" on the player's future at Arsenal's pre-match press conference ahead of tomorrow's trip to Everton.
Wenger, however, is confident when the time comes, Wilshere - touted as a future club captain - will sign on the dotted line.
"Jack has always been very committed to this club and I hope he will show that. There is only one way to show it and that is to commit your long-term future to the club," the Arsenal boss said.
Arsenal are now benefiting from their home-grown recruitment policy, which Wenger feels will make a strong bond between the developing players and their club.
"If the quality is local, it is of course even better because it gives you more guarantee of stability because the players who are English who play for Arsenal are more likely to stay for a longer term than foreign players, but we look first at quality, that is the most important," he added.
Walcott has recovered from a shoulder problem and should be in contention tomorrow night.
Wenger came in for criticism from some of the travelling support during the goalless draw at Villa Park on Saturday - with chants of "you don't know what you're doing" greeting the second-half substitution of striker Olivier Giroud for defensive midfielder Francis Coquelin.
However, the focus of the French coach remains unmoved.
"My job is to give full commitment to this club, with integrity. That's what I always do without expecting any return," he said.
"I don't want to comment on that [fans]. I just make sure that I do my job properly - that's what I do."