It was reported at the weekend that Tottenham Hotspur had turned down a world record bid in the region of £82 million for the Wales international.
Zidane, who has been installed as an assistant coach to Carlo Ancelotti, said: “If he has expressed a desire to join Madrid, then Tottenham should give him permission to speak with us.
“The chance to play for Real Madrid might only come around once in a player’s lifetime.
“And it is understandable Gareth does not want to miss out on it.”
Madrid are reported to be preparing a new approach in an effort to secure a player who was named PFA Player of the Year, PFA Young Player of the Year and Footballer of the Year in England last season.
Zidane added: “This is modern football. You have to pay to get the best players in Europe.
“Last season Gareth was on the same level as Ronaldo and Messi. The best players can have not so great games but change a game with a moment of brilliance.
“Those are the sort of players that win you Champions League and league titles.”
Having already signed Isco, Asier Illarramendi, Daniel Carvajal and Casemiro, Real have spent heavily this summer but Tottenham chairman Daniel Levy is believed to be demanding 145 million euros (£126m) for Bale.
Another Madrid affiliate, Sergio Ramos, adopted a more ambiguous tone with regards to the possibility of signing Bale.
Madrid captain Iker Casillas had hailed Bale as "one of the best three or four players in the world" but Ramos kept his cards close to his chest when asked by reporters whether Carlo Ancelotti's side needed to add Bale to their squad considering the enormous price Spurs are demanding for him.
"I think that the price of the player is dictated by the market," he said.
"It's not my job to decide whether we should sign Bale or someone else. It's important for Madrid to have a large number of young players and Spanish players in the team.
“The mix of youth and experience makes for a good project. The president and the other directors will decide whether or not we sign Bale, not me," he added.