The Bayern Munich winger has impressed at the tournament in Brazil under the management of Van Gaal, scoring three goals in as many appearances.
Van Gaal has also worked with Robben during his stint as Bayern boss.
"I think Louis wants him desperately to come to Manchester United," Roy told talkSPORT.
"Bayern Munich is also a big club and he is very happy there but you never know. With football, everything is possible."
Robben joined Bayern from Real Madrid in 2009.