Dutch MEP Derk Jan Eppink in September claimed that Bankia, which was last year bailed out by the Spanish government, paid part of the world-record fee and demanded an investigation into the matter.
But Perez on Thursday strenuously denied Bankia's involvement in the transfer, telling the Desayunos Deportivos de Europa Press: "We have not done a deal with any financial body, for the umpteenth time, as I've said ad nauseum.
"People in football know what's actually going on and what is not.
"Bankia did not pay for the transfer of Gareth Bale, we completed it using our own resources. The financial statement was made public and all our shareholders have a copy of it.
"Now it's said that they (Bankia) helped transfer Bale to us and it's a lie. Real Madrid paid for him with significant resources and I'm a little annoyed to have to speak about it."
Wales winger Bale arrived at the Bernabeu on September 1 and succeeded new team-mate Cristiano Ronaldo as the most expensive player in the world.
Real paid Manchester United 94million euros (£80m) for the Portuguese star in 2009.
But two days later Eppink tweeted: "Bankia finances 101 million Real Madrid purchase of Gareth Bale. Both Bankia and Real virtually bankrupt. Is European taxpayer who pays deal.
"I will file written question to Commission. Bankia 101 million Real-loan is distortion of Competition. Deutsche Bank can't do it for Bayern (Munich)."
Real are also one of seven Spanish clubs under investigation by the European Commission for Competition, which is seeking to determine if state aid received by those clubs is in line with European Union regulations.
Barcelona, Athletic Bilbao, Valencia, Osasuna, Elche and Hercules are the other clubs under investigation.
The Commission will also investigate whether the widely reported land transfer between the City of Madrid and the club Real Madrid in 2003 involved any state aid in favour of the club.
Perez added: "In regards to our business with the Ciudad Deportivo (Sports City training ground), there was a complaint and a subsequent investigation. They wanted to hurt us but nothing happened."