The England midfielder has not played a year due to knee and ankle problems, and will not be fit in time for the start of the 2012/13 campaign.
Wilshere has not travelled with Arsenal on their pre-season trip to Asia, and has not kicked a ball since undergoing surgery in May.
Wenger said: “I am positive but a bit cautious because we had so much disappointing news with him.
"Everybody in the medical department says to me he’s doing very well.
“He is still in the gym. Any player still in the gym in July is not on the pitch in August, that is for sure.
"I don’t want to give him any precise deadline because that would put him under huge pressure.
“At the moment, I’m trying to go step-by-step with him but the news is positive."
The 20-year-old had been expected to miss no more than a week when he suffered an ankle injury in pre-season last year, but he has suffered a series of setbacks.
“He had his ankle problem and that created a knee problem. He needed surgery on his knee tendon.
"The advantage of this was to heal completely the inflammation in the ankle. The ankle is perfect and the knee is doing very well. Normally he should go out again in a few weeks.
“It will take some time to come back but let’s not forget Jack is 20 and that means you recover quicker than when you’re 32.
"If he has no medical problem, he will come back very quickly.”