Van Gaal started work at Old Trafford last week after leading the Netherlands to third place at the World Cup and he is using the tour of America as a chance to assess his squad.
The Dutchman will also need to make a decision on United's next captain, with Rooney a contender for the role, and the England striker is eager to make an impact in pre-season.
"We all have to go out and show what we can do," Rooney, who could start United's first pre-season fixture against LA Galaxy in the early hours of Thursday morning, is quoted in The Sun.
"We have to show him every day in training what different qualities we have got as players and a team.
"Everyone wants to impress the new manager so that is what we are all aiming to do.
"We will try to put what we are doing in training into the games. Obviously, we have a manager with new ideas so we have to try to train well and make sure we are listening to what he wants to do and take that on to the pitch. We have to show him what we can do.
"I've only had one session but the preparation has been really good. I'm just looking forward to getting more sessions in before our first game."
United's record signing Juan Mata is also looking forward to the prospect of playing a full part in pre-season following Spain’s group stage exit at the World Cup.
Mata told MUTV: "It will be a different pre-season for me because in the last six or seven years I've always had a tournament with the national team and haven't had a complete pre-season with my team.
"So this time I will do the whole tour of the States, which is good for me to prepare for a long and hard season. This is my first pre-season with United and I'm enjoying it.
"It's the start of a new era for the club, with a new manager and players coming in. I'm really happy with the manager's style of football and hopefully at the end of the season we can celebrate something, which would be amazing for him and for us.
"We're focused on improving and trying to learn from the manager, to play at our best level during the season. The main idea is to play as a team and compete for titles."