The Sun reports that the Spanish giants could include Portuguese left-back Fabio Coentrao in a £50million deal for Bale.
Current Spurs boss Andre Villas-Boas tried to sign Coentrao for Chelsea last year.
Villas-Boas also wanted to include the 24-year-old in the deal that took Luka Modric from White Hart Lane to Real Madrid.
Bale signed a new five-year contract with Spurs in August.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?