Robinson, the son of Pro Basketball Hall of Famer David Robinson, suffered his latest concussion early this spring and has not practiced since.
"I think he understands that he's got to make a decision here pretty quickly, because we're going to go right into weight training next week," Kelly said. "We'll have some time off in May, and then we're back at it in June. So my expectation is that we'd have something here within the next couple weeks."
Kelly said Corey Robinson has met with Dr. Jeff Kutcher, the national director of the Sports Neurology Clinic, which specializes in sports concussion management and treatment.
"Corey had a meeting with Dr. Kutcher, who we feel is one of the best," Kelly said following the Irish's penultimate spring practice. "... His family was with him. And I think it was an extremely educational meeting for him. I'm very hesitant to go into the details because I think that's a private matter for Corey.
"But I know this: That he came back feeling really good about the meeting, and I think a decision will be forthcoming relative to what his future is. It was great that we were able to get him with somebody with that kind of knowledge, and I know he feels a whole lot better about that meeting."
Robinson was elected Notre Dame's student-body president in February. In a subsequent news conference, he said he had initially wrestled with the idea of returning to the football team for his senior year.
Robinson has the chance to graduate this May and explore other opportunities -- including becoming an ACE teaching fellow and volunteering in Brazil -- so he sought advice from family, teammates and friends, and said that his father told him to live in the moment and "take take advantage of the opportunities right in front of your face."
"And I almost let that slip by," Corey Robinson said then, "so that would've been a tragic mistake on my part."
The 6-foot-4.5, 215-pound Robinson played in 12 games last season for the Fighting Irish, catching 16 passes for 200 yards and a touchdown. With 65 catches for 896 yards and seven touchdowns during his 38-game college career, Robinson would be the leading returning career receiver for Notre Dame in 2016.
Also Friday, Kelly said that redshirt sophomore tight end Nic Weishar (high ankle sprain) will not play in Saturday's Blue-Gold spring game. In addition, redshirt sophomore defensive end Grant Blankenship has been suspended for a team rules violation, and it has yet to be determined whether Blankenship will return to the program.