The armband is still up for grabs at Old Trafford ahead of the upcoming Premier League season, following the departure of skipper Nemanja Vidic to Inter.
Darren Fletcher captained the side on three occasions during the club's pre-season tour, with Tom Cleverley deputising against Roma and Rooney leading the team against Liverpool on Monday.
"What I really like about Rooney is his attitude towards playing for United," Schmeichel told Sky Sports. "Wherever the manager tells him to play he will do that with a smile on his face.
"He realises his importance to the team and if he has to play in midfield, it's for the team. You get that with experience and matureness. So I think he's the obvious choice for the captaincy."
United have one more friendly fixture remaining against Valencia at Old Trafford on August 12, before hosting Swansea City in their Premier League opener four days later.