United manager Solskjaer believes Greenwood is one of the best finishers he has ever seen and he will give the 17-year-old his opportunity to shine when Astana visit at Old Trafford.
Greenwood has made four substitute appearances this season, but Solskjaer told reporters on Wednesday that the English teenager would start against the Kazakhstan champions.
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"He is still very young, Mason, but he's maturing," Solskjaer said. "He's developed so much in the last six months since I came in.
"I remember the kid who just wanted to play with mates in the Under-18s. And now he's knocking on a door, he's ready to play these games.
"For me, he has been in the Under-21s with England, he's tasting it more and more. And his appetite for football must be growing.
"I just don't want to put too much pressure on him, apart from go out there and enjoy yourself.
"I know he'll make the right finish. Keeper might make a fantastic save but he's one of the best finishers I've seen.
"It's just that enjoyment, express yourself, go out at Old Trafford because there'll be 11 Astana players living the dream tomorrow."
Solskjaer intends to change tack as his side embark on their Europa League journey as the manager focuses on the youth at his disposal.
He confirmed academy graduate Axel Tuanzebe, 21, will be in the line-up against Astana, 28 months since last starting a match for United at Old Trafford.
A knock sees Daniel James join Paul Pogba, Anthony Martial and Luke Shaw on the sidelines, with Fred coming into midfield and back-up goalkeeper Sergio Romero getting the nod ahead of David De Gea.
"It's a process and for these, we trust them. It's for them to grow as players but also human beings - that responsibility of being robust enough to go out at Old Trafford," Solskjaer said.
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"It's not just about enjoying yourself because you've got to get results.
"And if you don't throw them in you don't know what you've got so, for me, I don't see this as any other way of doing this because I've always done this wherever I've been.
"I've not been too many places but that's my belief as a coach that you have to give them a chance, an opportunity.
"Especially forward players. They'll win you games. Defenders it's a shift, find a way to win a game and keep them out."
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