Numerous reports have suggested that Mourinho will part company with Los Blancos at the end of the season even if he manages to guide the club to success in the Champions League.
Villas-Boas, 35, had been regarded as a 25/1 shot to fill the void at the Bernabeu at the start of the weekend. However, following a number of bets, the Portuguese coach can now be back backed at evens.
"Villas-Boas has silenced the majority of his doubters this season and follows in the mould of Mourinho with his football philosophy but lacks the overbearing ego, which has caused so many fractions in Madrid, so he could well be the perfect fit for the Bernabeu," Sky Bet football trader Chris Spicer told The Metro.
"The key to his success at Spurs has been getting the best out of Bale, so if the Welshman is their main transfer target this season, then acquiring his current manager would certainly do their chances no harm."
Villas-Boas took charge of Spurs last summer following a brief stint with Mourinho's former club Chelsea.