The current Netherlands coach, who recently announced that he will leave his post after the FIFA World Cup, is the overwhelming favourite to succeed David Moyes at Old Trafford.
And the Dutchman has further fuelled the speculation that he will take charge of the beleaguered Premier League outfit by labelling them the "biggest club in the world".
"I would love the job," Van Gaal told BBC Sport.
"For every coach who takes the job it's a fantastic challenge. I hope I shall be the one, but you'll have to wait and see."
Van Gaal's distinguished coaching career has seen him win domestic titles in his native Netherlands, Spain and Germany with Ajax, Barcelona and Bayern Munich respectively, as well triumph in the UEFA Champions League in 1994-95.
Should he get the United job, the 62-year-old will be tasked with turning the club's fortunes around following Moyes' ill-fated 10-month spell at the helm.
United's Premier League title defence never materialised - the side are seventh heading into the final game of the season - and a failure to secure Champions League football for next season proved the final straw for the club's owners.
Ryan Giggs was installed as interim manager after Moyes' exit last month and it remains to be seen what future he has at the club.
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