Domestic violence claims were made against the 20-year-old in a series of Instagram posts, which have since been deleted.
The Premier League side issued a response saying it was aware of the allegations that were circulating on social media.
The statement read: "We are aware of images and allegations circulating on social media.
"We will not make any further comment until the facts have been established.
"Manchester United does not condone violence of any kind."
Greenwood has been at Man United since the age of six and progressed through the academy into the first-team.
His first start for the club came in 2019 and he broke a number of records along the way.
When he scored against Astana in the Europa League, he became their youngest ever goal scorer in a European competition at the age of 17 years and 353 days.
The forward has scored 35 times for the club in 129 appearances.
He has also made one appearance for the England senior side after playing for the England under-15s, 17s, 18s and 21s.