Greenwood took his goal tally for the season to 15 in all competitions, including eight in the Premier League, with two goals as Manchester United brushed aside Bournemouth 5-2 at Old Trafford on Saturday.
The 18-year-old’s ability has often been compared to former Netherlands, Arsenal and Man United striker Robin Van Persie.
Solskjaer is adamant Greenwood is ready to break into Gareth Southgate’s squad following his impressive run of form.
"When you play for Man United, I think that's a test that's good enough and difficult enough," said Solskjaer, whose United are in the midst of a 16-game unbeaten streak.
"If you can handle playing for Man 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 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."
Manchester United are still in the hunt for a place in the Champions League and they travel to relegation-threatened Aston Villa in their next Premier League game on Thursday.
