The 62-year-old, who will step down as the Netherlands coach after this summer's football World Cup, reportedly agreed to a multi-year deal on Friday night.
De Telegraaf reported that the Dutchman, who has managed Barcelona, Bayern Munich and Ajax, would be given 100 million euros to spend on player transfers in the summer.
The newspaper did not identify the source of its information but a spokesman for United later denied that any deal had been done, saying: "There is nothing to report. We have not signed a new manager. When we have something to report, we will announce it."
United, the most successful side in the history of the Premier League and one of the most valuable sports franchises in the world, are currently languishing in seventh place and out of contention for highly lucrative European football next season.
The club on Tuesday sacked manager David Moyes, the hand-picked successor of the legendary Sir Alex Ferguson, only 10 months into a six-year deal.
Veteran midfielder Ryan Giggs will take charge of the side for the remaining four matches of the season, starting with tonight's contest against Norwich.
In comments made before the news broke about Van Gaal, Sir Alex said he believed Giggs was the ideal person to take over as the club's full-time manager.
"I think that he is the one man they should go to really," said Sir Alex.
"He's got 20-odd years of experience at Manchester United. I signed him as a kid at 13 years of age. He's gone through the gamut of emotions at the club - he's experienced all the highs and lows.
"He knows exactly what's needed to be a Manchester United player and I was so pleased he brought Paul Scholes back in, and Nicky Butt of course - two great professionals.
"They understand the club, they are hard workers, they are straight as a die. So you have got the right combinations there, there's no doubt about that."