The Red Devils thrashed Leeds 4-0 in Australia as part of their pre-season tour.
It comes as refreshingly good news to United, who are hoping for a better season than last.
The Old Trafford outfit finished sixth in the Premier League last time out and Solskjaer has been desperate to bring the good times back.
One of his main policies has been to incorporate the youth at the club and there are not many better prospects than Greenwood – who starred against Leeds today.
Here are five reasons why the youngster should start against Chelsea next month in United’s season-opener.
Greenwood showcased incredible speed against the Whites in a frightening attack spoiled for pace.
Him, Daniel James and Marcus Rashford started in a three-pronged attack that was too much to handle for Marcelo Bielsa’s men.
Against Chelsea’s ageing backline, Greenwood could provide the added legs to give the likes of Cesar Azpilicueta and David Luiz hell.
The 17-year-old is well-known in the academy for having a Midas touch in front of goal.
Last year, he netted 30 goals for the junior side and was in fine form against Leeds.
He opened the scoring against the Elland Road outfit within seven minutes as well as hitting the post twice.
The last thing Chelsea would expect is a fresh-faced teenager coming up against them on the opening day of the season.
Many of their plans would be geared towards stopping the more established stars at United, including Rashford, Romelu Lukaku and Anthony Martial.
What the Blues will not have planned for is the impact Greenwood could have.
Greenwood is desperate to play for the team he has grown up worshipping, such as the likes of Rashford, Jesse Lingard and Tahith Chong.
The youngster would be brimming with confidence to be given the chance to who up against Chelsea on the first game of the season.
And with Lukaku looking to leave the club, it would show all the fans that loyalty is rewarded at Old Trafford.
Solskjaer is a massive fan of Greenwood and said as much after the Leeds win, saying: “He’s got a chance of starting that one, definitely.
“He’s more than capable and will always be there, in and around the box, creating chances.
“And I won’t say that’s not a possibility, no, it’s a good possibility. If he keeps going as he does. It’s difficult to keep players out who perform well.”