The 20-year-old Leeds-born striker has been at Dortmund for just over a year and has produced an incredible 38 goals and nine assists in just 40 matches.
That follows on from a record of 29 goals and seven assists in 27 games for Austrian champions Red Bull Salzburg.
Haaland’s form over the past 18 months has seen him become one of Europe’s most sought-after under-21 talents, and he does not turn 21 until July.
Solskjaer worked with the striker at Molde and has long been confident that the forward will enjoy a successful career at club level and international level.
United and Chelsea are both understood to be huge admirers of the Norway international, who is available for £67million in 2022 due to a release clause in his Dortmund contract.
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The Red Devils wanted to sign Haaland from Salzburg before Dortmund beat them to the player’s signature, sealing a bargain £18m deal.
And Solskjaer, discussing his countryman’s progress in Germany, has dropped a major hint that United will go back in for him this year or next year.
“Erling will have a fantastic career. I’m following Erling. I’ve always said that,” Solskjaer told Norwegian outlet VG.
“Was it 18 months we had together or something? Almost two years, maybe. A wonderful time.
“He will definitely have a great career for both Norway and his club. He is doing incredibly well for Dortmund, so we’ll see where he ends up.
“As a Norwegian and someone who has worked with him, it is of course fun that he does so well. We will do what we can to become a better team and he will do what he can to become better player.
“Where does he end up? I don’t want to say anything other than that I wish him all the best. The choice he makes is up to him.
“He will have a long, long, long career that will surpass most of what Norwegian football players have experienced.”
Haaland has previously United boss Solskjaer the “perfect” coach and said about their time together at Mole in April of last year: “I was working almost two years under him and I have a lot of good memories.
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“Especially for young players, he was a perfect coach. Because he was an excellent striker, he taught me a lot of things.
“Even now we are texting sometimes and I am happy about his success with Man United. I wish him all the best for the future.”
Before that Haaland, whose father Alf-Inge played for Manchester City and Leeds United, said in 2019: “He [Solskjaer] has had a huge impact on my life, both as a person and as a trainer.
“He won the Champions League and was an incredibly good player. He has taught me a lot. I have dreamed of playing for the best clubs in the world my whole life, and I especially like English football.”
United will face huge competition from Chelsea and a multitude of other European clubs, however, with the Blues keen to recruit a top-level striker to catapult them into Premier League title contention.
Solskjaer’s charges have improved this season with Edinson Cavani leading the line but the Uruguayan turns 34 this Sunday and is out of contract in the summer.
United have an option to extend Cavani’s stay at Old Trafford by an extra year and are surely likely to do so given his impact thus far.
Solskjaer said on Boxing Day of the seven-goal forward: “At the moment, it looks like he has a few years left in him. So I wouldn’t say anything else.
“He has made a great impact when he has come here. Let’s focus on improving everyone but he has a few years left in him.”