Van Bommel played under the Dutchman for 18 months at Bayern Munich, but despite their shared nationality, it wasn't a case of the two having much in common.
The midfield general ended up leaving the Bundesliga for Italy after falling out with his compatriot in 2010, and warned that Van Gaal seeks absolute control of the culture of the clubs he manages.
"He [Van Gaal] wanted to change the whole club," the 38-year-old told Goal of Van Gaal's arrival in 2009. "It was a change of culture from the German to the Dutch.
"On the pitch he is good but outside it was a little bit difficult. He has a way and it is his way. He wanted to to straight. He doesn't want to go right or to go go left, only straight. Everybody knows what he wants.
"I had a little problem with him in 2010 in December and I went to Milan in January. I was the captain and it was strange to change clubs in the winter."
However, it is hard to argue against the idea that Van Gaal has been anything but good for the Manchester giants thus far.
United enjoyed a couple of strong spells of results in the Premier League last season, and, helped by his discipline and tactical organisation, looked as good as they have since Sir Alex Ferguson retired two season ago.
Additionally, Van Gaal has helped to coax the likes of Ashley Young and Marouane Fellaini into form after desperately disappointing campaigns last season.
But Van Bommel warned that the former Netherlands manager places too much emphasis on playing well, and not enough on securing victory.
""The Dutch way of coaching is we think how we can attack an opponent and defeat them," Van Bommel added.
"To be better with the ball and without it. To be better physically and technically and tactically. Every aspect of the game we need to be the best, we want to be the best. That is the Dutch way of thinking.
"Sometimes it is also to win ugly and go home. He wants to be better and better a better. If he loses and his team have played better then that is OK for him."