"It's scheduled right now to be done, ... we're going to be looking at it real fast, because obviously he's a big part of the now, as well as the future," Cooper said. "And he's kind of a special guy, he has a chance to be very good. And we want to make sure that we're doing everything in our power to make that happen.
"If you look at our track record, I bet if we're not the top in baseball, we're close to that in keeping guys healthy."
The MRI reportedly will be done Thursday.
Sale was one of the American League's more effective starters with a 3-1 record and 2.81 ERA before elbow tenderness led to the team moving him to the closer's role on Friday.
His first stint out of the bullpen was Tuesday, when he gave up an unearned run and blew the save in a 5-3 win over the Cleveland Indians. A source familiar with the situation told ESPNChicago.com's Bruce Levine that the MRI was scheduled before that outing.
Cooper told Bowden that Sale has soreness and stiffness and the team is going to continue to discuss his role in a couple of days.