United are said to have spoken to Greenwood over his discipline, specifically being late for training on several occasions.
The 19-year-old striker has been left out of the last two games against Newcastle and Paris Saint-Germain, with Solskjaer blaming his absence on a slight injury.
"We have a great tradition and history of bringing our players through," said the United boss.
"That means from early on you get good habits, we trust you and you express yourself. Mason has come through this programme, he's done fantastic and will be kicking on I'm sure. He's a very exciting boy to work with."
Asked if Greenwood has made a target of himself, he added: "You do when you play well. I'm not concerned at all with Mason making a target of himself.
"He came in, played fantastic, played his first league against Tottenham last season and was brilliant and just kicked on. Yes, he's made a mistake for England.
"He's a fantastic boy to work with. He's never, ever late for training. He's never a problem when he's at the training ground. He's always on time.
"We've got photographers outside the training ground every day so they can see he's on time every day.
"He's got a good family behind him, he's got a good background in the academy and he's a good trainer. He trains really well.
"I've seen some ex United players talking about him and they don't know what they're talking about. That's something we have to deal with. Many other players at United have had that."
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