The former Tottenham talisman has been heavily linked with a Bernabeu exit in recent months.
Bale was backed to join Manchester United in the summer, with Spurs also said to be chasing the crocked winger.
United boss Jose Mourinho publicly revealed his admiration for Bale, however, the Special One claimed a move would be ‘mission impossible’.
And according to Spanish transfer outlet Don Balon, Bale has an agreement with Florentino Perez to leave Real in the summer.
The say the Wales international wants to quit the Bernabeu and return to the Premier League.
Don Balon also say that United have tabled an offer for the injury-prone winger, 28.
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Gareth Bale next club: Latest odds
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“Gareth Bale will leave Real Madrid at the end of the season”
The Red Devils are only willing to pay around £53m for Bale, despite Real demanding around £80m for their star man.
Bale has struggled to impress under Zinedine Zidane this time out, with injuries halting his season.
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The winger has started just four La Liga games under the Frenchman, with Bale making two further appearance as a substitute.
Real are back in action on Thursday when Zidane’s men travel to Numancia in the Copa del Rey.