The Dutchman is currently CEO of Ajax, but there have been suggestions he would be open to a role at United in the future.
Scholes believes adding van der Sar as a link between the footballing and financial departments of the club would take the pressure of Ed Woodward, the club's executive vice-chairman.
"I think a director of football would take a lot of pressure off Ed Woodward, of course it would," he told Stadium Astro.
"I think Ed's very good at running the club and making money for the club. I'm not sure he has the knowledge of football that's required to go out and sign players and clearly there's been some issues in getting deals over the line.
"I think a director of football would be very good for him to take him out of the limelight a little bit.
"We don't seem to want to go down that road. Whether they've looked at people and they can't find the right person, I don't know."