Jones, 45, and Hassan, 42, were thought to be close friends, as they have both been involved in the local US football team Hollywood United.
However, according to The Mirror, Jones was given a "good hiding" by the former boxer after an exchange of jokes went "too far".
"When Tamer suggested it may be best to discuss their problem outside all hell broke loose," said a source. "It was like something out of a Wild West film. Fists were flying and at one point the two of them were grappling on the floor."
Celebrity Big Brother star Jones, who was left with an injured nose, has played down the incident. "Me and Tamer had words and a bit of a scuffle like a lot of blokes do on a weekend after a drink and a curry," the ex-footballer told The Sun. "We're making a movie together next week. It'll all be forgotten about by then."
Hassan's lawyers have stated that their client was subject to an "unprovoked attack" from Jones. "He regrets being put in the position of having to defend himself, but defend himself he did," they added.
Jones's rep commented: "Vinnie was having a business dinner when he got involved in an altercation. Following the incident he returned to his table. Yesterday he was playing football with his Hollywood team as he always does on a Sunday."