On transfer deadline day, FIFA refused to sanction the £22m transfer of Silva from Sporting Lisbon to Leicester after the paperwork was submitted 14 seconds late.
In the three weeks since the transfer deadline, Leicester's lawyers have been working on proposals to argue for an overrule and FIFA has received the club's proposals.
Silva has been training alone rather than with the rest of the Leicester squad and manager Craig Shakespeare is becoming frustrated with the situation.
Leicester are uncertain how their bid will be received by the football governing body but they hope that Silva will soon be available for selection, after the midfielder has been watching games from the King Power stands in recent weeks.
However, it may well be that the Portuguese midfielder has to wait until January before he can play for the Foxes.