The 20-year-old forward was arrested on Sunday after allegations were posted on the Instagram account of a woman who uploaded images of bruising to her body and bleeding from her lip.
A voice note purporting to be of an attack was also posted. The posts were all deleted from the social media site but were widely shared.
“Detectives have been granted additional time to speak to a man in his 20s who is being held on suspicion of rape and assault of a woman,” Greater Manchester police said in a statement on Monday.
“The suspect was arrested yesterday afternoon and remains in custody.
“Enquiries are ongoing and the victim is being offered specialist support. We remind people to avoid any commentary or sharing of images that could compromise the victim’s right to lifelong anonymity, or risk prejudicing a live investigation with active proceedings.”
United has said Greenwood “will not return to training or play matches until further notice.”
Greenwood, who has scored six goals this season, has a United contract through 2025.