The incident occurred in the Emporium wine bar in Clitheroe north of Manchester on Wednesday night and no one has been arrested, police said.
"It was reported that a 23-year-old local man had been assaulted by a 51-year-old man. He did not require hospital treatment," Lancashire Police said in a statement.
Moyes, 51, was not named but a source confirmed he was involved in the allegation.
"Inquiries are ongoing and we are speaking to a number of people to try to establish the circumstances," the police statement said.
"There are a number of differing accounts which we need to work through to try to establish exactly what has happened."
Moyes was fired by the English Premier League club after just 10 months in charge having presided over a disappointing campaign in which United finished.
He was linked earlier on Thursday with a return to management with Scottish champions Celtic after manager Neil Lennon stood down.