The former Red Devils goalkeeper, who won seven major honours during his time at Old Trafford, was recently tipped to take over in an upstairs role.
United are looking to bring someone in to act as a direct link between executive vice-chairman Ed Woodward and manager Jose Mourinho, with Roma chief Monchi and Fabio Paratici of Juventus also thought to be under consideration.
Van der Sar has ruled himself out of the running, however, telling The Sun: "I still have a two-year contract [at Ajax]. Ajax is my club and I would like to stay longer."
United reportedly want a new man in place to act as their transfer guru before the end of the season.