Madrid sports daily AS reported on Monday that football's governing body had requested information from Real on any foreign national players under the age of 18 registered in 22 youth teams with which Real Madrid have agreements.
"Firstly, we are in agreement with FIFA on this matter," said Buragueno at the unveiling of Brazilian midfielder Lucas Silva as a Madrid player on Monday.
"We are continuing to collaborate with them in everything they ask of us. We have peace of mind with the procedures at Real Madrid."
Barcelona are currently serving a one-year, two transfer window, ban on signing players handed down by FIFA due to irregularities in the signing of non-Spanish minors between 2009 and 2013.
Madrid beat off competition from around Europe to seal the signature of 16-year-old Norwegian teen prodigy Martin Odegaard last week from Stromsgodset.
However, Odegaard's move is not likely to fall foul of FIFA's rules as European players can move freely from the age of 16 as long as certain educational criteria are fulfilled.
Whilst Odegaard is expected to play out the rest of the season with Madrid's reserve side, Real Madrid Castilla, under the orders of French legend Zinedine Zidane, Silva insisted he is ready to be called upon immediately by boss Carlo Ancelotti.
The 21-year-old sealed a deal worth a reported €14 million ($15.8 million, £10.5 million) on Friday and arrives fresh from winning the Brazilian championship for the second consecutive year with Cruzeiro.
"I have had a week of pre-season training with Cruzeiro and I have done a lot of physical work," he said.
"This afternoon I am going to train with the first team to try and adapt as soon as possible."
The current Fifa investigation centres on two Venezuelan players, Manuel Godoy and Fernando Macías, who signed for Real Madrid when they were 12 and 14 respectively, according to AS.
Real Madrid parted company with Godoy in 2013 after suspecting his signing could lead to problems with Fifa and ended their relationship with Macías at the end of last season.
AS also reported that Real Madrid was not the only Spanish football club to be investigated by Fifa for underage signings, Atlético Madrid, Valencia and Rayo Vallecano will also be scrutinized.