The 51-year-old is thought haven been enjoying a meal at the Emporium wine bar in Clitheroe when the alleged incident occurred around 10pm on Wednesday evening.
The Emporium is located above an antiques shop in the centre of Clitheroe and is thought to be a short drive from his home.
Police are understood to be examining CCTV footage from the bar and speaking to people who were there at the time.
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 10pm yesterday (Wednesday, May 21st) 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.”
The former Everton manager was sacked as Manchester United boss in April and has since been replaced by Dutchman Louis van Gaal.
The Scot has kept a fairly low profile since his sacking and was thought to be a contender for the vacant manager’s job at Celtic following Neil Lennon’s unexpected departure from the club on Wednesday.