Cook is currently struggling with ankle ligaments problem that he picked up while on international duty with England’s Under-19 squad.
The midfielder is set to miss Saturday’s Championship encounter against Blackburn Rovers at Elland Road.
Redfearn has admitted that he does not know the extent of the injury suffered by the 18-year-old, and has revealed that the teenager himself thinks that it is not serious.
“Apparently, it’s ankle ligaments, he has strained some ankle ligaments,” the 49-year-old told LUTV. “I don’t know the severity of it.
“Lewis seems to think that it is a lot easier, which he would do because the kid wants to play. We have had it scanned, and the scan does show a strain but not a serious strain.”
Cook has been a regular for Leeds so far this season and is one of the best young players in the Championship.
The teenage midfielder has created 36 chances in as many Championship appearances this campaign, while having a pass accuracy of 75% and a shot accuracy of 50%.
Leeds are 13th in the Championship table at the moment with 52 points from 39 matches and are pushing for a top-10 finish this season.