The Borussia Dortmund striker is one of the most sought-after players in world football and the Manchester United boss - who coached the player at Norwegian club Molde - knew that he had the "personality" to reach the top.
Asked if he expected Haaland to progress in the manner he has, Solskjaer told Sky Sports: "Yeah. You can see the personality.
"He came as a 16-year-old, of course you never know with injuries, he struggled really badly with bad knees when he came. But I could see someone with a personality.
"I remember him brushing off and putting our centre-back and centre midfielders, two big, massive lads, he put them on the floor and asked them to get up. He's a winner."
Solskjaer continued: "He's got a great personality, of course. He's proving to everyone how good a player he is.
"We played against Zenit in the Europa League play-off and the referee came to me after and said, 'He'll play in the Champions League soon'. We did know.
"He's a top personality. I played with Alf (Haaland's father), he's a bit old school in that respect. He's a winner."
United are among a host of top clubs who have been linked with signing Haaland but Solskjaer remained tight-lipped on the speculation.
He said: "Erling will have a fantastic career. I'm following Erling. I've always said that. He is doing incredibly well for Dortmund, so we'll see where he ends up.
"We will do what we can to become a better team, then he will do what he can to become a better player."