The 18-year-old has shone since making his first-team debut 19 months ago, scoring 17 goals last season and going on to recently make his England debut.
But Greenwood was sent home from his first Three Lions camp for breaching their strict bio bubble in Iceland and he has reportedly been warned about his behaviour.
Time-keeping was mentioned as an issue but Solskjaer downplayed that talk as the teenager prepares to make his return against Chelsea this weekend.
He's a fantastic boy to work with. I have to disappoint you, he's never, ever late for training, he's never a problem when he's in the training ground
Ole Gunnar Solskjaer on Mason Greenwood
“He’s a good trainer, he trains really well, and I cannot believe all these stories about him not being professional,” the United boss said.
“You do (make a target for yourself) when you play well and I’m not concerned at all with Mason making a target of himself.
“He’s come in, he’s played fantastic, he played his first league game against Tottenham last season, was brilliant and just kicked on.
“Yeah, he’s made a mistake this summer with England and suddenly the whole English press go after him and that’s something we’ve got to look after.
“He’s a fantastic boy to work with. I have to disappoint you, he’s never, ever late for training, he’s never a problem when he’s in the training ground.
“He’s always on time. I’ve seen the stories, actually some ex-United players talking about him and they don’t really know anything what they’re talking about because, well, we’ve got photographers outside the training ground every day so they can check the time every day.
“I don’t know where these stories have come and I’ve just got to say he’s got a good family behind him, he’s had a good background in the academy.
“So, anyway, that’s something we have to deal with with many players, many other players at United have had that.”
Greenwood missed United’s impressive Champions League win at Paris St Germain on Tuesday with an unspecified issue, while captain Harry Maguire and new signing Edinson Cavani were other high-profile absentees.
Asked if the trio are available to face Chelsea on Saturday evening, Solskjaer said: “I hope and expect all three of them to be available for selection.
“Of course we’ve got a training session this morning but, yeah, they’ve all got a chance, all of them.
“There’s two different reasons, so Edinson wants to tick all the boxes that he’s gone through in his programme and feel ready to make an impact.
“I think his last preparation was going to be today and then I’ll have a discussion with him, and it seemed positive yesterday with both Mason and Harry.”