However, the Bayern Munich man rebuffed the offer, as he insisted that he is happy with the Bundesliga side.
"After the match he asked me to come to Manchester," Robben told Dutch TV station NOS.
"I'm very happy with where I am now. I told [Van Gaal] that. Van Gaal is the best coach I've had. We've got a very special relationship, but I will not make a transfer.
"I'm at the right place at Bayern so that has nothing to do with Van Gaal or United."
Robben was part of the Bayern Munich side that won the Bundesliga and the DFB-Pokal cup last season.