Florentino Perez added more fuel to the speculation linking the PFA Player of the Year with a move to the Spanish giant saying the Liga club likes the Welshman's profile.
Various reports suggest the Liga runner up is readying a mega-money offer to lure the Welshman out of White Hart Lane in a deal which could potentially match its capture of Cristiano Ronaldo.
Spurs are hopeful of hanging on to winger, though, and are said to be ready to offer the 23-year-old a new and improved contract to convince him to stay put.
"He's one of the big players out there in Europe and Real Madrid always likes big players," Perez told Punto Pelota."I met Tottenham chairman Levy last year and he has an obligation to defend their interests.
"Regarding the figures spoken about Bale, players are neither cheap nor expensive, but an investment. The most expensive players are those that can be classified as an investment because, if they are very good, they produce a return."The Blancos have also been linked to Malaga midfielder Isco, who is believed to be following former coach Manuel Pellegrini to Manchester City. Perez confirmed there have been no discussions over the Spanish attacker.
"Isco's father was in the club's offices recently, accompanying a representative of Malaga," continued Perez. "I had to do some business related to La Liga. We have not spoken to him or Malaga."