Here's what we know so far ... the Cleveland Browns running back went to the Barley House party spot on Saturday night with a bunch of friends and stayed late into the evening. 

Right after he left, SOMETHING happened -- and several cops went over to speak with the 23-year-old. He wasn't arrested. Wasn't detained. He left without incident. 

But, a witness tells TMZ Sports ... Hunt was involved in a physical altercation with another man before the cops came over. The witness wasn't sure if it was a "real" fight or if he was just horsing around with a buddy. 

At one point, one of the officers can be heard on video telling Kareem, "I saw him push you."

Barley House owner Bobby George told WKYC3 that Hunt was involved in a "small argument with one of his friends ... People blew it out of proportion."

We reached out to the Cleveland PD but despite the video, they have no record of the interaction -- "There wasn't a police report or any calls that we have located."

Either way, it's notable considering Hunt had publicly stated he was seeking help for alcohol and anger management in the wake of TMZ Sports posting video showing him in a 2018 physical altercation with a woman.