Forward Dan Cleary left practice on Tuesday, but Babcock said he didn't have an update on him.
Draper, who has an upper-body injury, did not play in the last two games of the regular season.
If Cleary can't play, it would probably be more of a loss than missing Draper, whose plus-minus rating was a team-worse and career-low minus-13 this season.
The second-seeded Red Wings begin their defense of the Stanley Cup on Thursday night at home against the seventh-seeded Blue Jackets. Columbus is making its first playoff appearance in franchise history.