Mason Greenwood of Manchester United celebrates scoring their fourth goal during the UEFA Europa League group L match between Manchester United and AZ Alkmaar at Old Trafford on December 12, 2019 in Manchester, United Kingdom.
Solskjaer's weakened side started the game sluggishly but four second half goals secured what turned out to be a comfortable victory, with Greenwood grabbing a brace.
After the match, Solskjaer praised the teenager, saying: "I've probably said it all before, so it's nothing new - that's what he does.
"And tomorrow he'll probably go in training and score a few more. He's always done it. That's just natural for him.
"He's a natural footballer but the closer he gets to goal, the more dangerous he is.
"Right foot, left foot - nightmare probably for defenders. He needs to develop his heading then he can be a proper striker."
Solskjaer compares Greenwood to Rooney
Solskjaer was asked if he had ever seen a striker as capable as Greenwood is aged just 18, and the Norwegian mentioned former United striker and club top goalscorer Wayne Rooney in comparison.
"I've seen a few good ones, yeah," he noted.
"I've played with Wazza myself. Obviously natural finishing, he's one of the best I've seen.
"I knew we had got a top talent there and I think this club is the best at recognising that and, for me, developing talent like this. There's no better place for him to be than here."
With United coming into the transfer window linked with Erling Braut Haaland and Mario Mandzukic, Solskjaer did not give the impression that Greenwood would find it hard to come by minutes on the pitch.
"He played against Tottenham and he was class," he said. "I'm not afraid of playing him in the Premier League. Not at all.
"But it's about sharing the minutes and finding the right minutes for him. Of course he is ready to play in the Premier League."
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