The 39-year-old Norwegian scored 91 Premier League goals for the Red Devils between 1996 and 2007.
He then went on to manage the club's reserve side for three seasons, before leaving to take charge of Molde in 2011.
"Maybe it sounds stupid but my dream is to manage United," Solskjaer told Marca. "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."
Solskjaer is considered by many to be an Old Trafford legend, having scored an injury-time winner for United in the 1999 Champions League final against Bayern Munich.