Stam, who previously managed Reading, spent three seasons at Manchester United, helping the club to the Champions League in 1999.
He has been out of a job since March having suffered a poor run of results with the Championship outfit.
Current Manchester United manager Jose Mourinho is under immense pressure at Old Trafford after a stuttering start to the season.
The Red Devils sit eighth in the Premier League table having won just five of their ten games so far.
Mourinho has also guided his side to just one Champions League win and an exit from the Carabao Cup at the hands of Derby.
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And Stam has revealed his desire to one day take charge at Old Trafford.
“I hope to work sometime for an absolute top club,” Stam told Voetbal Primeur.
“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.”
One of Stam’s former team-mates Andy Cole has admitted that legendary manager Sir Alex Ferguson could not return to the club.
“I don’t mind managers who have a go at me if that brings the best out of me,” Cole told the Guardian.
“Working with Sir Alex was an eye-opening experience.
“He was fantastic and the only manager I’ve ever come across who could manage different generations.
“But the way he spoke to us then would definitely not work now.
“The power is with the players now.”