The former Dutch center-half-turned-coach is said to want a position at United under head coach Ruben Amorim.
Stam, who is managing DOS Kampen in the sixth tier of Dutch football, won the Premier League, Champions League, and FA Cup with United in 1999, along with countless other trophies.
Speaking to Sport Lens, Stam said: "I’d love to coach at Manchester United but they haven’t picked up the phone!
"I think everyone who has been associated with the club would love to go back and help, having been in management myself I have coached and helping them in any role would be great.
"I’m always open for talks because I’d love to see the club back winning trophies and maybe I could help coach the defence.
"But with the manager lots of new staff has come in so they have plenty of options. But you never know."