Captain Thomas Vermaelen hailed the 21-year-old as "world-class" following another battling display in the Gunners' 2-0 Premier League home defeat by Manchester City on Sunday.
Wilshere - out for more than a year with ankle and knee injuries before returning to action this season - is likely to again be at the heart of the team when Swansea come to Emirates Stadium for Wednesday night's FA Cup third-round replay.
Given Mikel Arteta is set for a spell on the sidelines with a minor calf strain, Arsenal look set to rely on the combative young Englishman even more as his side head into a run of matches which could define the remainder of the season.
Wenger, though, is in no doubt Wilshere can meet the challenges head on.
"Let's not set any limitations. What is important is the day he will have made his career and thinks, 'I have been as good as I could have hoped to be'," Wenger told Arsenal Player.
"I have managed many great players in my life, the one common thing in their career is that they always wanted to improve. Every day they had 100% focus, they had that basic attitude right."
Despite the nation's high hopes for Wilshere - who has been at Arsenal since the age of nine - Wenger maintains the midfielder's game must be allowed to develop naturally.
"You want a player of such a young age to give him time as well. I believe the most important thing is that he has talent and loves football. As long as he loves football, he will improve," said Wenger.
"Let's keep that kind of important ingredient in the development of a player right, and not make them feel that they have nothing to grow for."
Wenger added: "In England the way to protect the players is to just let them develop naturally and not put too much pressure on them.
"Here, the expectation level is so high individually on players that they are not in a normal development, sometimes there is so much focus on them that I feel it is a handicap."
Wenger accepts there will come a point when Wilshere needs a break.
He said: "At the moment I don't think he is overloaded because he just came back very recently, and you get the feeling he gets stronger.
"We have a good approach taking the physical analysis and statistical analysis between what the player feels and what the medical department thinks, and you have to come to a conclusion on that.
"At the moment, all these three are positives, so I don't think I will rest him immediately, but it will happen."