Zidane, who coaches Madrid's second side, made the comments in the wake of speculation linking the Welshman to United.
It has been reported that Madrid are interested in United goalkeeper David De Gea and could send Bale to United in a swap deal for the 24-year-old Spaniard.
But as Los Blancos forked out 86 million pounds to sign Bale in 2013, Zidane believes that the 25-year-old is not going anywhere.
"Real Madrid buy the best players in the world. They don't sell them," Zidane was quoted as saying by the Daily Mirror. "Of course other clubs will be interested in him, he would improve any squad in the world, but the president has said he is not for sale and that is because he is not for sale.
"That will be the answer to Manchester United or any other club that asks the question.
"He was a big part of our success last season especially in the Champions League, and as we look to defend our title I am sure he will play a successful part again."