Chelsea and England defender Cole called the FA a "bunch of t***s" on Friday after he was accused of "evolving" his statement supporting John Terry's defence against the charge he racially abused Anton Ferdinand.
The 31-year-old later apologised "unreservedly" for his outburst, insisting he posted in "the heat of the moment".
The FA refused to comment on whether action would be taken against Cole but their own 'charging guidelines' in media comments and social networking cases are clear.
A breach of the rules includes: "Comments which are improper, which bring the game into disrepute, which are threatening, abusive, indecent or insulting."
Cole deleted the tweet but the FA guidelines add: "Deleting an inappropriate posting, whilst advisable, does not necessarily prevent disciplinary action being taken."
Several players have been punished for offensive tweets in recent times, including Rio Ferdinand for retweeting a comment describing Cole as a "choc-ice".
Chelsea refused to comment on what action they had taken against Cole although indicated manager Roberto Di Matteo might do so after Saturday's Barclays Premier League game against Norwich.