Toronto's closer has been out since April 21 because of inflammation in the affected area. He was tentatively projected to miss three to four weeks, but more than a month later and there is still no timetable for his return.
Santos has yet to throw off a mound. Although the club is optimistic that will happen by the end of the week, it's far from guaranteed.
"I think every time we've given you a time frame it has ended up being a little bit longer," Blue Jays manager John Farrell said. "I'd like to think he can get to that distance by the mid to latter part of this coming week.
"He has been out to 120 feet on flat-ground long toss with some aggressiveness. The kind of the earmark, or the threshold, with the flat-ground work is when he gets out to 150 to 175 feet and he passes that with no issues then the mound is the next step."
Santos, who is on the 15-day disabled list, has two saves in four opportunities this season. He was acquired from the White Sox during the offseason for prospect Nestor Molina but has yet to find his groove in Toronto.
Santos, 28, will eventually need to throw at least four to five bullpen sessions before going on an extended rehab assignment. In many ways, it's like starting Spring Training all over again, and as a result, he will not be back with the big league club anytime soon.
"Where the soreness is generated when he starts to get more aggressive, he'll feel a little bit in that same area," Farrell said. "We're taking baby steps to get past that pinpoint of the spot where he has felt it in the back of his shoulder."