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 (pictured) -- 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 go to Emirates Stadium for tonight'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 said.
"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 per cent focus, they had that basic attitude right."
Despite the 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."
3Arsenal v Swansea, ESPN, KO 7.30