Cleverley made 22 league appearances last term but struggled to find consistent form as United endured a miserable time of things under David Moyes.
However, the 24-year-old is confident he can flourish under Dutchman Van Gaal, who is preparing for his first season in the Premier League.
"I watched the manager's Holland team in the World Cup and from that I think I'm going to be his type of player," Cleverley said.
"I have to show that in training and most importantly games. I think there's a place for me but I have to prove it."
After missing out on a spot in Roy Hodgson's England squad for the World Cup, Cleverley claims to be refreshed.
"I managed to have a good break and recharge my batteries," he said.
"Now we're back and all trying to impress the boss.
"We know what he wants - a passing and moving style.
"He's very clear and we have a good group of lads who are willing to learn.
"We made a good start the other night [in a 7-0 win over LA Galaxy] and we'll see how we go from there."
United kick off the Premier League season on August 16 with a home game against Swansea City.