The 20-year-old has not featured for the Gunners all season because of a niggling ankle problem which was initially picked up on international duty with England and eventually needed surgery.
Speaking ahead of Saturday's Barclays Premier League trip to Stoke, the Arsenal manager said: "At the moment Jack has a different worry. His focus is to get back on the football pitch and play, there is not one specific target like the Olympics or the European Championships, although he is out of that."
He added: "His main priority is to get out on the pitch and play football.
"Nothing is definitely set at the moment, because we are in a slow progress world where we go step by step."
Wenger continued: "If we start pre-season at the beginning of July and he is completely fit to join in normal training, then we will see [about the Olympics], but let's not forget he has not played for a whole year.
"To be competitive at the top level it will take him some time to come back and we have to give him that time."
Source: PA
Source: PA