Bale joined Madrid from Tottenham in a world record £85.3 million transfer this month and scored on his debut at Villarreal 10 days ago.
Pérez says United's interest was irrelevant since Madrid had tracked Bale for two years.
"Signing the best players out there is Madrid's philosophy and Bale was the best available player on the market this summer," Pérez told Cadena Sur. "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."
Though United were interested in Bale, HuffPost UK understands no formal bid was submitted, although Tottenham did contact the Premier League champions offering the Welshman to them, albeit at a higher price than the one Madrid paid. United were also resigned to the fact Bale was determined to join Madrid.
Spurs and United's relationship suffered over Dimitar Berbatov's move to Old Trafford in 2008, when Sir Alex Ferguson met the Bulgarian at Manchester airport despite Tottenham's claims their striker had not been given permission to speak with United.
Tottenham chairman Daniel Levy's reputation as an uncompromising negotiator during that deal and Michael Carrick's £18.6m switch in 2006 also put Ferguson off from bidding for Luka Modrić.
Pérez who believes Bale came "cheaply", added Cristiano Ronaldo's contract negotiations were "easy".
Shortly after Bale signed, Ronaldo inked a five-year contract extension and stated he wished to finish his career with Real despite considering a return to United.
But Pérez 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."