Van Gaal is still awaiting his first competitive win as United boss since being appointed as David Moyes' successor, a role he undertook after guiding Netherlands to a third-place finish at the World Cup in Brazil.
United finished seventh last season have spent big in the transfer window in a bid to turn their form around, bringing in the likes of Argentina winger Angel di Maria in a British-record move and Colombia striker Radamel Falcao on loan from Monaco.
And Chelsea boss Mourinho, who worked under Van Gaal at Barcelona and cites the Dutchman as one of his managerial influences, has no doubts that the 63-year-old will reverse United's fortunes.
"He is one of the best managers in the world, so I think he is a man with great experience for the job," Mourinho told Eurosport-Yahoo.
"Manchester United is a big team, he is a big manager, so I think they will do well together."
By contrast to United, Chelsea have a 100 per cent record from their first three Premier League games and have already netted 11 goals.
Mourinho has adopted a more free-flowing style of play in his second spell at Stamford Bridge, although he warned it is likely to cost his side points during the campaign.
"It's a direction we tried to establish since the beginning of last season, but our squad now is different. We have different qualities now in our players," he added.
"The second season normally is a good season for a manager because you come from one season of work and you can choose a better direction you want to go and we feel comfortable and we feel happy the way we are doing things.
"Are we going to lose matches? Obviously, yes, but in this moment we are getting results and we are enjoying our style of play."
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