Van Gaal was unveiled to the media on Thursday after guiding the Netherlands to a third-placed finish at the World Cup.
Rooney told The Sun: "We have to show him [Van Gaal] 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."
United begin their tour with a clash against LA Galaxy in the early hours of Thursday morning.