The 28-year-old has emerged as a rumoured target for Craig Shakespeare's side during the final hours of the transfer window.
The Portuguese Football Federation (FPF) confirmed that he will return to the national team on Friday after being granted permission to leave.
"[Head coach] Fernando Santos and the FPF have authorised the player Adrien Silva to absent himself from the national team until Friday."
The Sporting midfielder will reportedly cost Leicester in the region of £22m if a deal can be finalised.
Portugal face the Faroe Islands on Thursday in a World Cup qualifying clash in Group B.