Perez reveals United made Bale bid
The 24-year-old forward moved to Real from Tottenham earlier this month for a world-record 100million euros (£85.3million) after negotiations that lasted the entire summer transfer window.
Bale scored on his debut against Villarreal but missed a Primera Division game against Getafe at the weekend due to thigh injury.
However, Perez insists the club did not pay too much for Bale and told Cadena SER radio: "Bale has come cheaply.
"Signing the best players out there is Madrid's philosophy and Bale was the best available player on the market this summer. We had been following him for two years.
"Tottenham did not want to sell. We learned that Manchester United had made an offer and we made one ourselves."
Key to Bale's switch to Madrid was the fact he would be fulfilling his boyhood dream, Perez saying: "Since childhood he had had the dream of playing for Real Madrid and he asked us to make it possible for him to come."
Shortly after Bale's move to the Bernabeu, Cristiano Ronaldo signed a three-year contract extension and stated he wished to finish his career with Real after a period when he was linked with a move away - and a possible return to Manchester United.
Perez said: "The renewal of Cristiano Ronaldo has been easy - he is determined to finish his career at Real Madrid.
"Cristiano never spoke of money with me."
Of Mesut Ozil, who made a shock transfer to Arsenal at the very end of the transfer window, Perez added: "It was the father of the player who made contact with Arsenal.
"No one leaves Real Madrid if they don't want to go."
Real Madrid coach Carlo Ancelotti expects Bale to be fit to make his home debut against Atletico Madrid on Saturday.
The Welshman was due to face Getafe at the Bernabeu last Saturday, but a thigh injury he suffered in the warm-up ruled him out of the match.
Madrid are due to host in-form Atletico on Saturday, with their visitors holding a 100 per cent record after five games and sitting two points ahead of Ancelotti's team.
Given Atletico's form, Ancelotti will be hoping to put out his strongest side, which would include Bale.
He told reporters at Real's press conference: "Gareth Bale trained individually today. He should be fit for Saturday's match."