The England forward insists that he is ready for the responsibility, but said that he would have no problem with Robin van Persie being named as skipper.
"I am interested in the captaincy," Sky Sports News quotes him as saying. "I've captained United a few times and to get it on a full-time basis would be great.
"I feel I am ready for [the captaincy], but it's the manager's decision.
"If he chooses someone else, then honestly I've got no problems with that. I will respect his decision. Robin is captain of his country, he has captained Arsenal and if Robin gets the nod to be captain, then I'm sure he'll do a great job."
Nemanja Vidic, who has served as United captain since 2010, left the club for Inter Milan at the end of last season.