The Scotland international underwent surgery this week to repair ankle ligaments that were damaged while the forward was on international duty last month.
"We need to make sure he comes back at the right time, not too early, not too late," the Sunderland Echo quotes Di Canio as saying. "Obviously, we all hope that, in pre-season, he can start with us again.
"But we don't want to push him in this sort of situation, otherwise it would put him in trouble. He's still young and he can be a very good footballer for the club for the next few years and we have to make sure he's OK.
"The specialist who did the surgery and the physio in the next two weeks will check again and give the right timescale."
The 26-year-old moved to the Stadium of Light from Wolverhampton Wanderers last summer.