Bale has been regularly linked with a move away from the Spanish capital in recent years, with a return to the Premier League as a Manchester United player seemingly the most likely destination.
The player's agent Jonathan Barnett recently suggested that it would take a world-record sum to prise the Wales international away from the Bernabeu, while also insisting that his client is happy at the club.
However, El Chiringuito TV journalist Eduardo Inda - via The Express - claims that the 28-year-old is now eager to leave Los Blancos at the end of the season.
Manchester United boss Jose Mourinho has previously distanced himself from bringing in any more attacking players this summer, but both he and the club are long-term admirers of Bale and could explore the possibility of a deal should he become available.
Madrid president Florentino Perez is expected to conduct a major overhaul of his squad this summer following a hugely disappointing season so far, with the likes of Cristiano Ronaldo, Karim Benzema and Isco among those to have also been linked with an exit.
Bale has once again been troubled by regular injury problems this season, limiting him to just 17 appearances across all competitions so far.