The Sun says Bale, 23, still has three years to run on his contract and Tottenham want him to sign a new £170,000-a-week deal. But Madrid are prepared to hand him £10m a year and can also offer guaranteed Champions League football.
Their only demand is that he submits a transfer request to allow them to make formal contact and begin negotiations with his agent.
Real president Florentino Perez knows that Levy is a formidable negotiator and will not give up on Bale without a fight.
That is why he wants Bale to adopt the stance taken by Luka Modric, who forced through a £33m move to Madrid last year despite having four years left on his Spurs contract.