The Scot, who was sacked as Manchester United boss in April, is allegedly the 51-year-old man involved in an altercation at a wine bar in Clitheroe on Wednesday evening
Moyes, 51, is understood to have been involved in an altercation at The Emporium wine bar in Clitheroe on Wednesday evening.
Police said that a 51-year-old man was under investigation regarding the incident but have not confirmed it to be Moyes.
Lancashire police said in a statement: "Police are investigating a report of an assault at the Emporium wine bar in Clitheroe.
"Officers attended the bar at about 22.00BST on Wednesday 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."