The Welshman, who moved to the Bernabeu for a then world record fee of £85m in 2013, has often found himself consigned to the periphery under Zinedine Zidane.
Bale was set to complete a move to Chinese side Jiangsu Suning last summer in a deal which would have seen him earn £1m a week, only for the deal to fall through.
According to the Daily Mail, the 30-year-old has had enough of being left out under Zidane and will seek a move away from Madrid over the next summer transfer window.
Despite his clear unpopularity with Zidane, it was reported that Bale had no desire to leave Madrid over the summer after his move to China collapsed, with the winger and his young family settled in Spain after six years in the country.
Madrid, who have set their sights on signing Harry Kane from Tottenham Hotspur, are reportedly exploring the possibility of a swap deal which would see Bale return to North London.