The newspaper reports that the pair had to be separated after a heated exchange in a car park outside the West Hollywood nightspot, with Liverpool striker Andy Carroll acting as peacemaker.
However The Sun quote a witness as saying: “There was no row, no confrontation. They spoke but that was it. There might not be much love lost between them but there was no trouble.”
Tensions have been high between the pair since Cole acted as a witness in John Terry's trail for racially abusing the then-QPR defender. Terry was eventually found not guilt, but received a four game ban from the FA.
Requests made by the Sun to both Cole and Ferdinand's representatives for a comment didn't yield a response.
Ferdinand spent last season on loan with Turkish outfit Bursaspor last season, and has been on holiday in America following the end of the season.