The Sunday Mirror says Real believe they can tempt Bale to quit England - because of his growing reputation as a diver.
The Tottenham winger, who has picked up five yellow cards for play-acting since last season, reckons he is being victimised by match officials.
He has told friends that Madrid is his first choice if he ever leaves White Hart Lane and Bernabeu chiefs are now growing in confidence that they could sign him at the end of the season.
Bale believes he is being singled out by Premier League referees, and Madrid intend to use his growing frustration to their advantage. Spurs are sticking a £60million price-tag on the head of their Welsh international, but that will not deter the La Liga giants from stepping up their interest.
Cristiano Ronaldo's future is uncertain as he is being linked with a big-money move to mega-rich Paris Saint-Germain and, if he leaves, Bale will be Real's No.1 choice to replace him.