The 62-year-old is set to leave his post following this summer’s World Cup in Brazil and is keen to succeed David Moyes at Old Trafford, so long as United want him.
Van Gaal said: “I would love the job. I hope that I shall be the one. It’s the biggest club in the world and it’s a fantastic challenge.
“You have to wait and see what the club decides.”
Interim player-manager Ryan Giggs is expected to remain as part of the coaching staff, though is yet to confirm whether he intends to continue playing next season.
Van Gaal, who has won league titles in Spain, Germany and Holland, would be free to take charge after the World Cup, which concludes on 13 July. The Premier League season begins on 16 August.