Cole claims to have been the victim of racist 'monkey' taunts from Millwall fans, while Jason Price was also reportedly targeted by home fans during the Carling Cup tie between both clubs at the Boleyn Ground on Tuesday night.
The FA are aware of Cole's allegations and they will be looked at amid their thorough investigation into the events of the night.
In the meantime, football's 'Kick It Out' organisation believes the game will have suffered another "depressing development" if racist chanting allegations against both players are proven.
The tie, which West Ham won 3-1, was marred by three pitch invasions with fans also confronting police inside and outside the ground on a night of shame for English football.
One man was also stabbed as fighting between rival fans took place outside the ground.