Solskjaer had already warned him about his conduct following his expulsion from the England squad last month. Greenwood has now been late to training twice, reports The Sun.
But the teenage star has now been axed from the last two United squads for the 4-1 win at Newcastle and midweek triumph over PSG.
Solskjaer has also grown sick of the striker's general attitude so far this season.
His performance level has dropped significantly too not least in the 6-1 drubbing by Tottenham in United's last home game at Old Trafford.
Solskjaer claimed ahead of the PSG game that it was not a disciplinary issue and that he was out the squad because he had a 'niggle'.
The manager, however, refused to say what that 'niggle' was or when he got it.