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 up as a late replacement for a friendly to be played at Old Trafford against Denmark three days later.
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.
