The teenage forward further enhanced his reputation with a couple of clinical strikes in United's 5-2 win over Bournemouth on Saturday.
That brace took his tally for the season to 15 goals in all competitions, making him the youngest United player to reach that mark since record goalscorer Wayne Rooney.
Solskjaer was keen to play down comparisons to Rooney and fellow club legend Cristiano Ronaldo after the match, but he has backed Greenwood to shine for both club and country.
"When you play for Manchester United, I think that's a test that's good enough and difficult enough," he told reporters. "If you can handle playing for United, then you can handle playing for any team and Mason's got the qualities that not many others have.
"So he could play for England full team or the Under-21s, I don't really mind. I know he's doing well for us and it's great to have him here.
"Mason's a naturally good finisher, so he'll always score goals. He's a humble boy, he wants to learn, he listens and he works hard.
"Mason is one of the best if not the best finisher I have worked with and seen. He is so calm. He knows where to finish if it is on the training ground, here or in his garden at home."
Greenwood, 18, has been capped four times by England at Under-21s level. body check tags ::