The playmaker featured sparingly in the Premier League last season under David Moyes but is focused on Japan, rather than forcing his way into the Dutchman's thinking
Kagawa only started 14 Premier League games under David Moyes last season and made four appearances off the bench.
But rather than use the World Cup as a platform to impress Van Gaal, the playmaker is keen to focus solely on Japan.
"I think everyone knows I want to do well at the World Cup, and I'm sure everyone else does, too," he said, according to the Kyodo news agency.
"But I don't want to get my priorities mixed up here - the important thing is for Japan to win at the World Cup. I'm not using the World Cup as a place to showcase myself for [Van Gaal]."
Van Gaal was officially named Old Trafford boss on May 19, but Kagawa said the announcement was no surprise to the United players.
He added: "We've known for some time it was going to be him. We've got the World Cup first so I'll deal with all that after this is over."