The 30-year-old right-back was charged for stamping on Manchester United's Adnan Januzaj towards the end of Saturday's 3-1 defeat at Craven Cottage.
The incident was not seen by referee Lee Probert or his assistants, so Riether became the first player to be charged by the FA under a new pilot scheme where a panel of three former referees reviews video evidence of incidents not seen by match officials.
The German full-back apologised for stamping on Januzaj via his official Twitter account on Tuesday, adding: "I will accept the consequences of my actions, and hope to put it behind me when I return."
However, despite Riether's admittance of guilt, it is understood the club did not accept the charge before Tuesday's 6pm deadline.
Fulham have instead asked for clarification on certain points of the newly-instigated rules that govern when action can be taken.
The possibility of Riether escaping punishment would be a serious embarrassment to the FA, whose chairman Greg Dyke only last month admitted that the rules were flawed.
Dyke spoke out after the body's decision not to take action against Chelsea striker Fernando Torres for scratching Tottenham defender Jan Vertonghen.
"When millions of fans watching on TV can see an incident like this and the FA does not take action it is understandably baffling to everybody and has to be addressed," Dyke told the
Leaders in Football conference.
"For the FA's disciplinary department to find itself in a position where it is not able to take action against an obvious scratch just can't be right.
"What this means is, despite the rules being changed in the summer, they clearly weren't changed enough.
"As FA chairman I don't like to be in a position where I cannot explain the rules when action should be taken when something is pretty obvious."