According to Spanish paper El Confidencial, the La Liga giants are gearing up a massive transfer deal to bring the Welsh wizard to the Bernabéu.
Spurs chairman Daniel Levy will be offered £85m for the star and has already spoken in the past of the high price needed to prise the 24-year-old away from White Hart Lane.
The interest shown in Bale by Premier League Champ Manchester United is thought to have sparked Madrid into action.
David Moyes is poised to make a big statement in the transfer window and United had planned to lodge a £60m bid for the winger.
Moyes said at a press conference in Yokohama today that another offer had been lodged following chief executive Ed Woodward's return to England.
Moyes said: "As I understand it, Ed had a response (to the first offer).
"We have made a second offer but Ed is dealing with it rather than me."