Real seem to have lost patience with Bale as he continues to battle injuries, with the latest issue coming just before the international break.
Manchester United have tracked Bale since his Tottenham days and would move for the attacker should he become available.
Chelsea too are credited with an interest in the transfer, but the Express claim Bales suitors will be disappointed.
Bale is happy in Spain and will resist any effort from his club to offload him next summer.
Zinedine Zidane wanted to sell Bale in the summer of 2017, but Real overruled the managers attempts.
Bale responded to Zidanes criticism by starring for Los Blancos in the Champions League final against Liverpool, coming off the bench to score a crucial brace.
United have kept tabs on Bale for the last three years, while Chelsea are expecting to lose Eden Hazard to La Liga in the next 12 months.
Hazard has made no secret of his desire to play for Madrid, and could come in as a direct replacement for Bale.
Chelsea would jump at the chance to bring Bale back to the Premier League, while Tottenham too would be keen on a homecoming for their former talisman.