Perez claims United made a bid for Bale before the 24-year-old joined Real Madrid for a world-record fee.
Bale joined Real Madrid from Tottenham in a £86million deal earlier this month.
Perez told 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.
“Since childhood he had had the dream of playing for Real Madrid and he asked us to make it possible for him to come.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.