The Sun says the striker will get his chance against Kazakhstan side Astana.
Boss Ole Gunnar Solskjaer is concerned about his side's lack of firepower.
United have scored once in each of their last four games, securing just one win, at home to Leicester on Saturday.
It is the ideal chance for Greenwood, who turns 18 in a fortnight, to shine.
The youngster has come on as sub in four of United's Prem matches.