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The 39-year-old Norwegian himself wore the English team's shirt for over a decade, and later worked as a reserve team coach.
In recent years, Solskjaer has successfully led his native Norway's "Molde" team and has earned a reputation as a promising strategist.
"It may sound strange, but my dream is to coach 'Man Utd.' Although I'm not saying it will necessarily happen," said Solskjaer.
"I worked with Sir Alex Ferguson for 15 years as a player, and later as a coach. His methods had a huge influence on my football philosophy. I learned almost everything from Sir Alex. We both have self-confidence, always want to win, understand the meaning of hard work, and trust young players.