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The 18-year-old produced clinical finishes in either half as United thrashed Bournemouth 5-2to briefly move into the Premier League's top four.
Only Michael Owen, Wayne Rooney and Robbie Fowler have scored more Premier League goals in a season while aged 18 or younger and that trio all went on to feature for England on multiple occasions.
Bradford-born Greenwood has represented his country at various youth levels, debuting for England Under-21s last September,andSolskjaerbelieves he is on track to make the step up to Gareth Southgate's seniorside.
Asked if he was "a future England striker", NorwegianSolskjaertold BBC Radio 5 live: "Definitely, if he keeps on developing.
"We'll do our best to develop him. I'm just worried about him playing for Man United, not England.
"There might be some Norwegian blood in there, I don't know! I don't think so."
Solskjaeradded of Greenwood: "He's a great talent, great finisher and he's learning more and more, growing more and more, making better and better decisions on and off the pitch.
"He's an exceptional finisher, he can score right foot, left foot.If he can learn how to head aballhe'll be the complete striker."
United are now unbeaten in 16 games in all competitions, a streak thatdatesback toa home loss toBurnleyon January 22.
This latest victory saw United temporarily displace Chelsea in fourth only forthe Blues to beat Watford later on to reclaim their spot withSolskjaerinsistingthere is still a long way to go in the race for Champions League qualification.
"I don't think anyone worries or cares about that now, we've got so many games left," he said.
"Five games left - we know we have to focus on every single one of them at one time because you can only beat the team you're playing against.