After the clubs reached an agreement last month, FIFA blocked the transfer of the 20-year-old to the Primera Division side because of an administrative mistake.
A statement from Eibar read: “Sporting Club Eibar have appealed to FIFA regarding the international organisation’s decision not to grant them the transfer of Rafa Paez due to an administrative mistake that has now been corrected.
“Eibar handed all the documents from Liverpool for the transfer of Rafa Paez on January 30, within the deadline established by FIFA.
“However, FIFA notified Eibar on February 2 that an administration error had occurred in the process and that it was necessary to correct, something which was done immediately.
“A few days after FIFA announced to Eibar that the transfer had been denied.
“Eibar has presented an appeal to FIFA in order to be granted the transfer.
“Rafa Paez continues to train normally with the team, awaiting for this problem to be resolved in order to be available for selection.”
Paez joined Liverpool on a free transfer in the summer of 2013 after terminating his contract with Real Madrid.
The Spanish central defender played the 2013-14 campaign with the Liverpool reserves and was sent on a season-long loan to Serie B side Bologna last summer, where he made eight league appearances.
Paez was keen to return to Spain and play in the Primera Division for the first time.