The 28-year-old from Victoria had 60 per cent of the meniscus removed from his left knee last week after a freak accident that saw him step on a sprinkler head indentation at the Jays' training complex.
The initial prognosis was Saunders might be out until the all-star break in mid-July. But after surgery last Friday, that was adjusted to five-to-six weeks.
In addition to playing catch with head trainer George Poulis, Saunders has been tracking pitches in bullpen sessions.
"It's really surprising because when it first happened we thought 'oh-oh,'" said manager John Gibbons. "But he's moving along pretty good."