The 39-year-old Norwegian spent more than a decade with the Red Devils as a player, then went on to manage their reserves.
And Solskjaer, now winning admirers as coach of Molde, believes he has enough in common with Sir Alex Ferguson to suggest he can step into the 71-year-old's shoes when he finally retires.
He told Marca: "Maybe it sounds stupid but my dream is to manage United. But I am not saying it is going to happen.
"I worked with Alex Ferguson for 15 seasons as a player and then as reserve-team coach.
"His methodology has influenced my philosophy. Almost everything I know I learnt from Sir Alex.
"Both of us believe in ourselves, we always want to win and we put our faith in youngsters and work hard."
Meanwhile, former United goalkeeper Peter Schmeichel has told Jose Mourinho to forget about succeeding Ferguson.
The former Chelsea boss, whose Real Madrid side take on United in the Champions League on Wednesday night, is widely expected to return to England next season.
But Schmeichel told El Mundo: "He will not be the successor. I don't think the club would be happy with everything Mourinho brings with him.
"He's a great candidate for his qualities as a manager but the club doesn't want all the things that come with him."
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