Local reports have named Harry Maguire as being involved in an incident, but no details have yet been confirmed.
The England defender Maguire is on holiday in Greece.
Maguire joined United from Leicester for £80m – a world record fee for a defender.
“The club is aware of an alleged incident involving Harry Maguire in Mykonos last night,” United said in a statement on Friday.
“Contact has been made with Harry, and he is fully cooperating with the Greek authorities. At this time we will be making no further comment.”