On Sunday, Greater Manchester Police revealed that "a man in his 20s" had been arrested on suspicion of rape and assault after a number of social media posts from his girlfriend.
Greenwood, who remains in custody, has since been suspended by his Premier League club and been removed from computer game FIFA 22.
On Tuesday evening, Greater Manchester Police released a further statement, saying that the Englishman now faced two further charges and that an extension for questioning had been granted.
It read: "Detectives have been granted further additional time to speak to a man in his 20s who was arrested on suspicion of rape and assault of a woman.
"The suspect was detained in custody on Sunday (30 January) afternoon after we became aware of online social media images and videos posted by a woman reporting incidents of physical violence.
"He continues to be questioned after magistrates authorised an extension until tomorrow (Wednesday 2 February).
"Following enquiries so far, he has since been further arrested on suspicion of sexual assault and threats to kill."
Man United have already confirmed that Greenwood will not feature in training or games until further notice.