The Red Devils manager believes the teenager has enough potential to have a bright future with the national team
The 18-year-old produced clinical finishes in either half as United thrashed Bournemouth 5-2 to 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, and Solskjaer believes he is on track to make the step up to Gareth Southgate’s senior side.
Asked if he was “a future England striker”, Norwegian Solskjaer told 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.”
— Manchester United (@ManUtd) July 4, 2020
Solskjaer added 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 a ball he’ll be the complete striker.”
United are now unbeaten in 16 games in all competitions, a streak that dates back to a home loss to Burnley on January 22.
This latest victory saw United temporarily displace Chelsea in fourth only for the Blues to beat Watford later on to reclaim their spot with Solskjaer insisting there is still a long way to go in the race for Champions League qualification.
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“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.
“The next one is [Aston] Villa, we’ll have a good look at them tomorrow and recover and prepare for that one.”