“He is starting to jog this week.
I would think two to three weeks,” Wenger was quoted as saying by British media on Sunday.
“I spoke to Roy Hodgson and I told him that Wilshere will be available for England. He will be just polished for England.
“Jack can be the positive surprise.”
The foot fracture was just the latest injury blow to hamper the talented 22-year-old midfielder, who made his Arsenal debut as a 16-year-old in September 2008.
He missed the entire 2011-12 campaign and Euro 2012 after injuring his ankle in a pre-season friendly.
Wenger felt the injury experiences would aid his young midfielder in the long run.
“It is the most difficult thing in the world to deal with. You need to be competitive which is to always been in competition,” the Frenchman said.
“Jack has been in and out this year, but I think they have sorted out the problem now. I hope from now on he will always be available.
“Jack is a football man. He is the kind of guy who if you speak to him about anything, he has a natural football understanding.
“He watches the game and he analyses very well what is going on, and on that front he has learnt when he has been injured, from watching the games and from the problems you can face in the game.”
Wilshere watched Arsenal beat Hull 3-0 away on Sunday to keep ahead of Everton in the battle to finish fourth in the English Premier League and take the last Champions League qualifying place.
They host Newcastle United and West Bromwich Albion before finishing their league campaign at Norwich City on May 11 with the FA Cup final following at Wembley six days later.
Hodgson is set to name his 23-man squad to take part in Brazil on May 13.
England open their World Cup campaign with a Group D encounter against Italy in Manaus on June 14, followed by matches against Uruguay and Costa Rica.
(Writing by Patrick Johnston; Editing by John O’Brien)