Stam's last managerial role was at Reading.
He told Voetbal Primeur: "I hope to work sometime for an absolute top club. It should be no surprise that Manchester United are a dream club for me.
"That was the situation during my playing career, and it is still the case."
The Dutchman played 127 times for the Red Devils between 1998 and 2001, winning the Premier League in each of his three seasons at the club.