The video appears to show Barkley having a seemingly friendly conversation with an unidentified man, who then punches him twice.
It comes after Everton manager Ronald Koeman warned the England star on Sunday that he will be sold if he refuses to sign a new contract at the club.
The video, which circulated on social media, appears to show Barkley having a seemingly friendly conversation with an unidentified man, who then punches him twice before being restrained by bystanders.
"Merseyside Police is aware of footage online reportedly showing an assault in a bar in Liverpool city centre," police said in a statement.
"No report of an assault has been received, but officers are making enquiries to establish the circumstances of the incident."
Everton are yet to comment on the incident, which is said to have occurred hours after Barkley, 23, starred in their 4-2 home win over Leicester City in the Premier League on Sunday.