Marca says Real are hopeful that Bale will leave on loan.
They know nobody is likely to pay their £100m asking price for the forward, who has endured a nightmare season so far.
As a result, the loan market is seen as a way to get him off the books with Real supposedly hopeful any suitors will pay a small fee, pay the player's wages and have an option to buy on any potential transfer permanent.
Real management are hoping Manchester United will jump at the chance to bring the star in.
Chelsea and former club Tottenham will also be offered the chance to take Bale off Madrid's hands.