The Premier League club have been blocked from playing their £22m summer signing due to FIFA regulations.
The world governing body did not grant the International Transfer Certificate because the documentation regarding the move from Sporting Lisbon was filed 14 seconds after the deadline.
Silva has been training at the club, but is currently ineligible to play for the 2015-16 Premier League champions.
A statement from a Leicester spokesman read: "It was our intention to submit an application to the Court of Arbitration for Sport for expedited proceedings so that the matter could be resolved as quickly as possible.
"However, it has been made clear to us that FIFA will not support an expedited process, forcing the club to reluctantly accept the single-judge ruling of FIFA's Players' Status Committee without reasonable opportunity for independent arbitration that is timely enough to be effective.
"Our frustration at the denial of effective due process doubles our disappointment at the original outcome and while the club is now essentially powerless to continue to challenge the decision, we will continue to support Adrien in any personal appeal he wishes to undertake.
"We intend to register Adrien at the earliest opportunity. In the meantime, he will remain under our care, training with the squad under the supervision of our coaching, medical and sport science staff."
Silva may have to wait until January to play his first game for Leicester.