Bale has suffered 21 different injuries as a Real Madrid player and has been nicknamed ‘The Glass’, because of a series of ankle and calf problems.
The Welshman only played seven times for Zinedine Zidane’s team this season.
Madrid are willing to let 30-year-old leave the Bernabeu in January.
The Spanish giants would be interested in offering him, as a makeweight to bring long-time Paul Pogba to Spain.
But United have also been put off by the money it would take to reach a deal with Real.
