Manager Louis van Gaal is tasked with picking a new skipper for the 2014-15 Premier League season following the departures of Nemanja Vidic, Patrice Evra, Rio Ferdinand and Ryan Giggs' retirement.
Rooney - one of the frontrunners for the armband alongside Robin van Persie - officially threw his hat into the ring in the lead up to England's FIFA World Cup campaign in Brazil.
Two months on and the United striker has again put his hand up for the role following Van Gaal's decision to name Darren Fletcher captain in Wednesday's 7-0 rout of the Los Angeles Galaxy.
"Of course I would like the captaincy but it's the manager's decision who he chooses," Rooney said ahead of the club's second United States tour fixture against Roma on Saturday.
"I think he wants to work with the players and then choose a captain from there.
"I don't think he was ever going to just walk in and choose a player from the off. I'm sure he will look at the players now and make his decision in a couple of weeks."
Rooney did not wear the armband against the Galaxy but he was at his best, scoring twice in the first half as the Van Gaal era opened in resounding fashion.
And he is confident United can make up for their seventh-place finish last season by lifting the trophy.
"We can win the title. Last season was a bad one, we know that, but we are confident we can put it right. We have to believe we can win the title," said Rooney.
