Wilshere, 25, broke his leg during a 4-0 defeat at Tottenham Hotspur last weekend and will be out until after the end of his loan deal.
Wenger told reporters he had discussed the situation with medical staff.
"They think it's a very simple fracture, that doesn't need any surgery at all. Hopefully he will be back in July for normal training," he said. "But we need patience. Let's hope that all goes well.
"Until the end of the season he's a player of Bournemouth but we have a good understanding with the medical staff," added the Frenchman. "The rehab will certainly be made here...because the loan spell ends at the end of the season."
The injury-prone Wilshere has made 27 league appearances for Bournemouth during his season-long loan deal, his biggest run of domestic outings since the 2013-14 season.
Once one of the brightest young hopes in English football, Wilshere slipped down the pecking order at Arsenal after managing only 17 games in two seasons blighted by prolonged spells on the sidelines.
However this season was looking brighter and Bournemouth manager Eddie Howe said this month that he wanted to sign the player, who is entering the final 18 months of his contract with Arsenal, on a permanent basis.
Wenger said negotiations with Wilshere had yet to start and the injury had nothing to do with any extension although he had been saddened to hear of it.
"Jack is a great football player, a great football brain and his career has been stopped by many injuries," he said. "Today at the top level the most important thing is the consistency of the presence.
"When the player has been out for a while, the game is of such intensity that it takes you always a while to find the rhythm, the confidence back. A great career doesn't suffer stop and go. You have to be consistently present.
"When you look at all the players who are at the top level in the world like (Real Madrid's Cristiano) Ronaldo, they play 50 or 60 games a year. They have the luck not to be stopped by injuries. so you are always sad when a guy of that quality is stopped by problems."
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
Share
