According to the Spanish news outlet, the Red Devils have tested 'Los Blancos' resolve for the winger.
Real are seriously considering the offer as they realise this could be the last opportunity to make a profit on the man they signed for a world record £85m in 2013.
The emergence of young talent Marco Asensio has not helped the 28-year-old's case at the Santiago Bernabeu. The youngster outshone Bale in Sunday evening's 2-2 draw with Valencia, with Asensio scoring both goals for Zinedine Zidane's side.
Jose Mourinho seems determined to sign the Welshman and is making a final push before the transfer window slams shut on Thursday.