The departure of Nemanja Vidic to Inter Milan this summer has left United needing to appoint a new skipper and manager Louis van Gaal is taking his time before making a decision.
Robin van Persie, who was van Gaal’s captain for the Netherlands, is a contender for the job, while long-serving midfielder Darren Fletcher wore the armband in the midweek win over Los Angeles Galaxy.
Rooney, who scored twice in the 7-0 romp, has captained United in the past and he is hoping to be given the role on a more permanent basis.
“Of course I would like the captaincy but it’s the manager's decision who he chooses,” said Rooney.
“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.”
United finished last season in seventh as David Moyes failed to see out the season and van Gaal has been charged with the task of turning the ship around.
And Rooney said: “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.”
Rooney has been impressed by the initial impact of van Gaal and was also happy with the 3-5-2 formation which United played against LA Galaxy.
“In Brazil I watched the way Holland were playing and I carried on doing that when I came home,” said the England striker.
“However you can watch as much as you want but it’s when you hear him getting his point across in training that you start to learn.
“Louis van Gaal has been great. I’ve only had a few days but he’s a strong guy who has been good in training and it’s been enjoyable.
“He is bringing in a new style of play and wants us all to adapt to that and that’s been enjoyable.
“He’s very honest in training. If you are not doing well in training he will tell you but if you do well he will praise you. If you aren’t doing things right in training you need to know so that you can put them right.
"It's great to hear him say he wants to play two strikers as we have a few. It's a good formation and it's good to work on it in training for a few days."