While Giggs is not expected to be handed the job on a long-term basis, Bruce believes that the 40-year-old may be considered if he guides the team to four wins out of four.
"If they win the next three or four games 4-0 there'll be a clamour for Ryan I'm sure, and you wish him the best of luck," Bruce said in Friday's press conference.
"He has nothing to lose and no pressure on him, the supporters will be right behind him. He might win the next four games and give them something to think about."
United cannot mathematically qualify for next season's Champions League campaign as they currently reside seventh in the league table.