Club director Emilio Butragueno confirmed Fifa had asked the Spanish Federation for documents relating to transfers over the last five years.
Butragueno said the club was "absolutely calm" about its behaviour.
Fifa handed Barcelona a transfer ban until 2016 after they breached regulations when signing 10 players under the age of 18 in 2013.
In a statement, Real Madrid said the majority of the 51 players that world football's governing body had asked for information on were exempt from regulations for various reasons.
Fifa rules state that international transfers are only permitted for players who are over the age of 18 - unless the player in question meets one of three qualifying criteria.
Under-18s can move to a club in a different country if:
Real claim 10 of the 51 players were Spanish nationals, while 23 foreign players had already been registered with a Spanish club.
On Thursday, Real completed the £2.3m signing of 16-year-old Norway midfielder Martin Odegaard from Stromgodset.
Barcelona are not allowed to sign any players in 2015 after their appeal against their transfer ban was dismissed in December.
Fifa is investigating Real Madrid's youth transfer policy and has asked the club for information on 51 players.