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.
Manager Louis van Gaal is expected to decide between Rooney and Robin van Persie, though the Dutchman gave nothing away during the club's pre-season tour of the United States.
"What I really like about Rooney is his attitude towards playing for United," said Schmeichel.
"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."
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