The 62-year-old, who will lead the Netherlands in the World Cup this summer, has been widely tipped to take over at Old Trafford.
Ryan Giggs stood in for the last four games of the season after the sacking of David Moyes.
"I would love the job," Van Gaal told the BBC on Wednesday. "I hope that I shall be the one. It's the biggest club in the world and it's a fantastic challenge."
"You (reporters) are thinking I'm the man but the most important thing is whether Manchester United are thinking that."
Moyes was fired just 10 months after replacing Sir Alex Ferguson, with United standing seventh in the Premier League.