The 18-year-old, along with Manchester City starlet Phil Foden, came under fire after breaching quarantine protocol while on international duty.
While in Iceland, they invited two women up to their hotel room - where they were supposed to be isolating.
The pair have been reprimanded by manager Gareth Southgate after allowing model Nadia Sif Lindal Gunnarsdottir, 20, into the hotel.
She was also joined by 19-year-old law student cousin Lara Clausen after the Three Lions beat Iceland 1-0.
Foden and Greenwood spoke with the pair before inviting them up, where footage was then captured by the girls and spread on social media.
Both players were subsequently sent home as punishment for breaking Covid-19 regulations, a day after making their full international debuts.
Greenwood has been training on his own while back at United's training complex.
This was down to the fact he may have been a coronavirus risk to the rest of the squad, while he has made a personal apology to Solskjaer.
According to The Sun, the youngster now awaits his fate as United prepare to take on Crystal Palace in their Premier League opener.
Solskjaer is also reported to have had stern words with the forward, but there is no chance of any form of long exile from the squad.
In fact, Greenwood may even start against Palace after showing a positive attitude in training.
The Red Devils coach, though, may deem in necessary to banish the teenager from the matchday squad as a lesson.
Solskjaer knows all about the strict control in the dressing room from his time under Sir Alex Ferguson.
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And he is keen to replicate that environment as he plans on using Greenwood in a more advanced role in the first-team.
The England international broke onto the scene last season, forming a deadly partnership with Anthony Martial and Marcus Rashford.
Greenwood scored 17 and assisted five in a breathtaking campaign for the teen.