Telegraph reckoning Real Madrid are preparing to test the water with a £50 million summer bid.
The Spanish giants have requested to be notified should the Welshman become available, with the clubs president Florentino Perez prepared to offer £50m for the winger.
Real Madrid enquired about Bale when they signed Luka Modric from Tottenham in the summer, only to be told he was not for sale at any price.
Tottenham manager Andre Villas-Boas has admitted Bale may be forced to leave the club should they fail to qualify for the Champions League this season, and Bayern Munich have already been credited with an interest.
Perez is set to stand for re-election at the end of the season, and wants Bale to be the marquee signing to ensure he is given another four-year term.
However, Perez is aware that signing ‘the left footed Ronaldo’ as he is known in Spain, will be no easy task.
Meanwhile, Real also revealed that former midfield icon Zinedine Zidane will take a youth team coaching job at the club next season, with the long-term aim thought to be that he will one day manage the senior squad.