Robin van Persie has been touted as a possible skipper due to the pair's relationship from their time together with the Netherlands, while Darren Fletcher wore the armband during Thursday's 7-0 win over LA Galaxy.
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"Of course we can win the title," he told reporters. "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.
"Of course I would like the captaincy but it's the manager's decision who he chooses. 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."
Van Gaal opted for a 3-5-2 formation in his first game in charge and Rooney says the new manager's techniques are already coming across in training as the new season approaches.
"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," Rooney continued.
"He is bringing in a new style of play and that's been enjoyable. It was good to see it work [against LA Galaxy].
"In Brazil I watched the way Holland were playing and I carried on doing that when I came home. 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.
"He's very honest. 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."