The 52-year-old, currently in charge of Championship promotion-chasers Derby, faced Van Gaal during spells in Holland and Germany and is full of admiration for his counterpart.
McClaren said: "Without a doubt he has what it takes. He has a strange reputation. He's very forthright.
"He knows what he wants. He knows what he's doing and he's very disciplined. I've also heard that you either love him or you hate him - he's one of those characters.
"He is successful, he gets teams winning and he's experienced at that level. He can manage top players and win things at the top so he's a perfect fit for any of the top five clubs in Europe.
"Van Gaal is the only man I've ever had to present flowers to. In my first season in Holland, he was manager of AZ and I was manager of Twente.
"They had won the league and we were second. It was a game we had to win to finish second and they'd already won the league, so we thought we'd shower them with love and hope they'd lie down and die and give us a result.
"We made a procession for the players and I presented Van Gaal with a bunch of flowers."
Van Gaal remains the long odds-on favourite to become United boss this summer, despite Ryan Giggs kicking off his interim tenure with a 4-0 victory over Norwich.