The fallen Premier League champions are on the lookout for a new manager after David Moyes was sacked in April, just 10 months into a six-year deal.
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And former Wales assistant coach Verheijen believes the 62-year-old is the right man to return United to their glory days.
"Van Gaal is extremely keen to take a job in the Premier League," Verheijen told the Daily Mirror.
"Van Gaal is a team builder from scratch and like a teacher. I think he would be perfect for Manchester United.
"The fact there could be as much as £200m to spend on new players is a huge attraction.
"If most of that money had already been spent in the last year then I think it would have been less interesting to take this job.
"Then he might have to deal with players he might not have bought himself."
Verheijen was critical of Moyes throughout his brief tenure at Old Trafford, using Twitter to voice his disapproval with aspects of the 51-year-old's coaching and tactics.
While claiming Moyes was out of his depth in Manchester, Verheijen said United officials should take responsibility for appointing the wrong manager.
"You really wonder if the people who are responsible at Man United are actually doing their homework," he added.
"I don't think it is so much the problem and responsibility of David Moyes.
"But if the people at United had done their homework they would never have appointed David Moyes, they would have appointed someone else.
"When you are managing Man United you need different tactical qualities to when you are an underdog like Everton.
"It has to do with tactical flexibility."