Rooney has scored 11 goals in 16 appearances for club and country this season, playing a key role in United's revival after a disastrous start to the campaign.
Van Gaal believes the 29-year-old has benefited from the responsibility of wearing the armband for United and for England, but is adamant that a coach with his skills can improve any player.
“Before I came here, of course, I had heard of his reputation,” Van Gaal told reporters. “But, from the first day, he was not the Wayne Rooney that people had talked about.
“He was, in my eyes, a great example in training and, of course, he has achieved a certain level. I think he shall always play with me — although, when he is in a bad moment, maybe I can be convinced to change him.
“But he is my captain now. He is the men who sets the example for the other players. So I’m very pleased. I have the impression that he lives for football and that he likes being the captain of Manchester United.
“Of course, being captain of England helps him to be a better captain of United.
“He has more experience. But I have to remind everyone that I put him first as captain. Roy Hodgson followed my advice.
“I can make every player better. I’m sorry. That’s arrogant, but I can.”