Officers were called to the upmarket Emporium bar in the rural market town of Clitheroe, Lancashire, on Wednesday night following a report that Moyes was involved in an altercation with a 23-year-old local man.
It is understood Moyes, 51, had been socialising with his friend, Blackburn managing director Derek Shaw, a local businessman in the Ribble Valley who was on the board at Preston when the Scotsman was in charge at Deepdale.
Police said the 23-year-old man did not require hospital treatment following the incident at about 2200.
A spokesman said: "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 is believed that police will also view any available CCTV footage to try to shed further light on the incident.
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."
The fashionable town centre bar in Moor Lane bills itself as "half coffee shop, wine bar and brasserie; half interior design superstore", which offers "an unique, intoxicating lifestyle experience".
Moyes was dismissed by Manchester United last month following a mediocre season after he replaced the retiring Sir Alex Ferguson.
On Thursday, he was among several names linked with the vacant Celtic managerial position after Neil Lennon stepped down as boss of the Scottish champions.
He has formerly managed Everton and Preston, and played as a centre-half for a number of clubs including Celtic.