Greenwood, 18, has scored nine goals for United in all competitions this season and he is the club's leading goal scorer in the Europa League with four goals.
His eye-catching performances have led to calls for him to be handed his senior England debut and included in the squad for the Euros but Solskjaer said the youngster first needs to focus on improving himself.
"I think Mason will have a top and long career," Solskjaer told reporters ahead of Wednesday's FA Cup third round replay with Wolverhampton Wanderers. "Let the boy settle in now first before we talk about England and the Euros.
"His focus has to be on playing more for us, improving. When he plays more for us that'll happen by itself. He's just been picked for the Under-21s so he's focusing on his football."
Despite losing two strikers -- Romelu Lukaku and Alexis Sanchez -- to Inter Milan in the off season, Greenwood, Marcus Rashford and Anthony Martial have stepped up to deliver but Solskjaer refused to accept praise for their performances.
Rashford, who made his 200th appearance for United over the weekend, already has 22 goals for club and country this season while Martial has scored 11 goals in all competitions.
"I don't want credit, they're working hard to improve their game, all done well," Solskjaer added. "Mason's in his first season, so to have nine goals in not 20 appearances is fantastic.
"Marcus is growing and improving all the time and Anthony has missed eight weeks. I'm impressed by them, working well on finishing patterns. We want consistency and we'll see more and more of them."
Solskjaer confirmed captain Ashley Young would miss out with injury but was hopeful that long-term absentee Eric Bailly, sidelined since July with a knee injury, would be fit for Sunday's clash at league leaders Liverpool.
"He's very close, he might be back for the weekend," the Norwegian manager said. "We've got a game arranged today for the reserves, hopefully he will get 90 minutes. So (he) might be ready for Liverpool." (Reporting by Rohith Nair in Bengaluru, editing by Pritha Sarkar)