The Foxes were granted an extension to last week's 11pm cut-off point on deadline day in order to push through a transfer for the £22m-rated Portugal international.
Sporting and Leicester were confident that the move would successfully go through, but the necessary paperwork supporting the deal has been rejected.
City are now working closely with the Primeira Liga club in the hope of correcting the registration forms, though for the time being Silva's future remains in limbo.
"We are working with Adrien and Sporting Club de Portugal to overcome some issues relating to the player's registration and exploring all options to find a resolution," a Leicester spokesman said.
Silva missed Portugal's 5-1 win over Faroe Islands last Thursday to finalise talks with Leicester and has remained in England since.