That is exactly what Gerrard is predicting for the youngster, who is set to become his midfield partner for this evening's friendly with Scotland at Wembley.
"It's every kid's dream to captain your country," said Wilshere.
"I grew up watching David Beckham. He was my role model.
"It is up to whoever is in charge but that would be a dream come true."
Before it comes to pass, Wilshere evidently has to put his fitness problems behind him.
Injury has limited the highly-rated Arsenal star to just seven caps since his debut three years ago.
Not that Gerrard is too concerned by that unfortunate record.
"Jack is so good I am sure when he gets to my age he will be sitting in my position with the armband on talking about another 100-cap player," said Gerrard.
"I've got no doubt he can (be the man who succeeds him).
"It's his quality, his example in training every day. He wants to learn, he loves England. He ticks a lot of boxes when it comes down to other players following his lead.
"I've been in a similar position, I missed a World Cup and many caps.
"I'm really paranoid about putting too much pressure on any player but he is that good there is nothing for him to worry about."
Wilshere himself admits to an enormous sense of frustration about his England career, which has largely been spent in front of the TV cheering on the players who should be his team-mates.
Of his seven appearances, only one game - against Brazil at Wembley in February - and a further 13 minutes as a substitute in Sweden, have been on the same pitch as Gerrard.
"I've got a room where I've got shirts up; Stevie's shirts up and my seven caps," said Wilshere.
"Playing for England is the pinnacle. Missing matches has not been a good experience.
"I am yet to play in a World Cup match and haven't contributed anything to this qualifying campaign.
"But I want to help and I watch every game like a fan."
With Gerrard embarking on what is likely to be his last campaign as an England player, Wilshere is the player upon whom so many of England's future hopes rest.
However, having seen how much pressure has been placed on Wayne Rooney's shoulders in recent years, he is eager for the load to be shared.
"I've said many times we need to share the responsibility out," said Gerrard.
"As a nation we want to pin all the pressure on one person like we did with Gazza and we have done with Rooney lately.
"It's not dangerous, it's just not fair for one person to carry the nation's pressure.
"Eleven players go out there and you go to a tournament with 23 or 24."