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.
Read the full article on eurosport.co.uk: Wilshere expected back at training for Arsenal in July - Wenger