Van der Sar, 45, spent six seasons at the Premier League giants, in which he lifted four Premier League titles and the UEFA Champions League before retiring from football.
Since ending his playing days, the Netherlands legend has since taken up a board room role at the club he started his professional football career with and has been lauded for his restructuting of the Eredivisie side.
The Red Devils are reported to be keen on luring him to the Theatre of Dreams for the current vacancy of the sporting director role in order to work with new manager Ole Gunnar Solskjaer.
"I know United is a much bigger challenge than Ajax," the 130-time capped Dutchman told the Sunday Times. "United is not just a big and famous club, but also a worldwide brand — yet when you're inside it's still a family place.
"I remember when I came from Fulham. Oh it's United... but after one day you felt at home. The washing ladies. Mike the chef. Kath [the receptionist]. They're still there.
He added: "You need to cherish that and Ole [Gunnar Solskjaer] is doing a great job at it. But also Ed [Woodward].
"I have utmost respect for him, what he does for the club. So I don't need to be the big man. I want to feel I contribute, and you can only do it for something you believe in.
"United is a special place. Who knows, eventually? But for the coming years I'm here."