Smith, 23, was arrested and questioned by police earlier this month but not charged after an investigation into the incident during a League Cup match against Manchester United in October.
His arrest on November 13 prompted the FA to drop him from the national side hours after he was called
England went on to lose 3-2 but the episode led to a players' protest before the match.
Lawyers from the Crown Prosecution Service said last week they had advised police not to charge Smith with a criminal offence as it would not be in the public interest.
Smith has until December 9 to respond to the FA.