An incident between Moyes, 51, and a 23-year-old man is said to have happened in Clitheroe, Lancashire, at about 10pm yesterday.
A spokesman for Lancashire Constabulary said: "Police are investigating a report of an assault at the Emporium wine bar in Clitheroe.
"Officers attended the bar at about 10pm yesterday and 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.
"Inquiries are ongoing and we are speaking to a number of people to try to establish the circumstances.
"There are a number of differing accounts which we need to work through to try to establish exactly what has happened. No-one has been arrested at this stage."
It was reported that Moyes was having a drink with a friend when an "alleged minor scuffle" broke out in the bar.
Moyes was among several names linked with the vacant Celtic managerial position after Neil Lennon stepped down today as boss of the Scottish champions.
Last month he was sacked by Manchester United after a disappointing Premier League campaign.
He has formerly managed Everton and Preston North End, and played as a centre half for a number of clubs including Celtic.
A spokesman for the Emporium said: "There was an incident outside the building. However, it did not affect any of our customers or staff and has been dealt with by the police."