The 20-year-old was arrested by Greater Manchester Police (GMP) on January 30 after pictures and videos detailing physical abuse against an 18-year-old lady were posted on social media.
Greenwood was also questioned over threats to kill.
He was released on a bail condition that would have expired on April 30 but it has been extended until the middle of June.
Greenwood has been suspended from all first team activities by Manchester United since the allegations came to light.
“Update on rape investigation after social media images and videos posted online in January,” a GMP statement read.
“We are continuing to investigate a report made to us on Sunday 30 January of online social media images and videos posted by a woman reporting incidents of physical violence.
"A 20-year-old man arrested that day on suspicion of the rape and assault of a woman, and threats to kill, remains on bail.
"An application has been made to the courts to have his bail extended beyond Saturday 30 April, but the hearing isn't expected to be until mid-June.
"The suspect will remain on conditional bail until the date of the court hearing.
"Any update on the outcome of that hearing – or news before then – will be issued proactively by GMP press office."
Greenwood, who has one cap for the England national team, has scored six goals in 24 appearances for Manchester United this season.
