The Liverpool manager believes that, despite Van Gaal's experience of winning titles in Holland, Spain and Germany with clubs such as Ajax, Barcelona and Bayern Munich, he will be surprised when the Premier League kicks off again on August 16.
Van Gaal, who arrived in Manchester fresh from leading Holland to the semi-finals of the World Cup, has enjoyed a strong start to life at Old Trafford with his side unbeaten so far in his first pre-season campaign.
United beat Liverpool on their way to winning the International Champions Cup in Miami, but Rodgers has warned the Dutchman that life will be much harder when the domestic season gets under way.
"I think what he'll find is the competition in this league will be different to any other league that he's worked in," he said.
"In a lot of the other leagues, there are one or two teams and those are the teams that are expected to win.
"This is a league where the top team plays the bottom team and on any given day you can lose. You don't get that a lot in the other leagues. I think the competition will probably take him by (surprise), and that's from foreign managers I have spoken to over the years."
Despite the fierce rivalry between the two clubs, Rodgers also admitted that he is an admirer of van Gaal and what he has achieved in his career.
"I've obviously been an admirer of his work and his career," he added.
"He's a very experienced manager and a very good manager who has worked at some big clubs.
"When you come through as a coach, you look at the guys who have a vision and a philosophy, and he was obviously one of those guys."