The Netherlands coach described United as the "biggest club in the world" and said he 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," he told the BBC from the Dutch squad's pre-World Cup training camp.
But he said nothing had been agreed about him taking over at Old Trafford.
"You (the media) are thinking I'm the man but the most important thing is whether Manchester United are thinking that," he said.
The 62-year-old has been the favourite to take over at United since David Moyes was sacked last month after 10 months in charge.
British media have reported that Van Gaal's appointment could be confirmed next week but he could not begin work at United until after the World Cup and he said the speculation would not affect the Dutch team's campaign in Brazil.
"I have to focus on my job," he said.
"I am coach of the Dutch national team. I have waited a long time to be in a World Cup, so that's very important.
"This doesn't affect me. I have always had offers. I know what the football world is and what it means."
Van Gaal has won domestic titles in the Netherlands with Ajax Amsterdam and AZ Alkmaar, in Spain with Barcelona and in Germany with Bayern Munich. He also led Ajax to the European Cup in 1995.
United, seventh in the Premier League table, have endured a disappointing season, their first of the post-Alex Ferguson era.
Moyes lasted 34 league games before being replaced on an interim basis by Ryan Giggs who has led them to two wins and one defeat in his three games in charge.
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- Manchester United
- David Moyes
- Van Gaal