Several reports Friday said the 6-foot-4 inch, 250-pounder spent the night in the Cleveland Clinic because he complained of feeling ill for several days.
Further tests and evaluation have been recommended.
Coach Romeo Crennel revealed the details about Winslow Friday, but had no knowledge about when he would be released.
Citing patient privacy laws, the Akron Beacon-Journal reported that Crennel did not provide specifics about Winslow's illness.
"His arms and legs aren't falling off or anything like that," Crennel told the newspaper. "We know that he'll be out there (Monday) if at all possible (and) if it's possible that he can be there, he'll be there."
To date, the Browns' 2004 first-round draft pick has one touchdown after 19 receptions for 170 yards.