Van Gaal will now take over as manager of United while former Real Madrid and South Korea coach Guus Hiddink will take over the Dutch team for the second time ahead of the Euro 2016 qualification campaign.
"I have a special bond with him," Robben, one of the stars of the Dutch campaign in Brazil, said of the veteran coach. "He is the most important coach in my career. After the match he did ask me to come to Manchester."
It was not clear how serious the offer was, but Robben, who could be seen laughing while speaking about it, added: "It is not an option. I will stay at Bayern Munich."
Robben, who scored three goals in the World Cup, was in superb form in Brazil and is on the short list for the "Golden Ball" award presented to the tournament's best player.
United were on the verge of signing him from PSV Eindhoven in 2004, when he met then manager Alex Ferguson, but the Dutch club said the offer was too low and Robben joined Chelsea.
He later joined Spanish giants Real Madrid before moving to Bayern, for whom he scored the winning goal in the 2013 Champions League final against Borussia Dortmund.
(Writing by Steve Tongue; editing by Sudipto Ganguly)
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