The Wales superstar was linked with a move to Old Trafford during the summer transfer window.
Bale is a long-term target for United executive vice-chairman Ed Woodward.
Jose Mourinho is also keen and Starsport understand he was on alert to launch a swoop last month.
Speculation over Bale’s future at the Bernabeu has ramped up in recent months.
He suffered an injury-hit campaign last term and has competition from Isco and Marco Asensio for a place in Zinedine Zidane’s team.
But Perez insists the club are delighted to have Bale on their books.
The Bernabeu bigwig said on Cadena SER: ”[As for Bale], he is one of the best players we have and we are very pleased with him.
"There were no offers for him and what [Jose] Mourinho said about him was just said in a complimentary way.
"Every player is transferable right now and we'll see what happens in a year, although I don't know what'll happen next year, just as nobody does."
Bale is under contract until 2022 after signing a six-year deal last October.
He joined Real from Tottenham for a then world record £86m fee in 2013.