The star forward has long been linked with an exit from the Bernabeu with his £650,000-a-week wages a stumbling block.
He came close to joining Chinese Super League side Jiangsu Suning last summer before the deal collapsed.
And Marca claim Zinedine Zidane does not want Bale in his squad next season, and are willing to let him leave for nothing to get him off the wage bill.
The Wales international’s contract expires in 2022.
Former club Tottenham and Manchester United could reignite their interest, having previously been linked with a move.
Bale has scored in two Champions League finals for Madrid, winning four of Europe’s top prize, along with three Super Cups, three Club World Cups, one Spanish Cup, one Spanish Supercup and a La Liga title.
But his unwillingness to learn Spanish and his love of golf has not endeared Bale to the fans at the Bernabeu.
He has scored 105 goals in 249 appearances.