The Old Trafford club have twice bid in excess of £100 million for the Wales international, but their offers have been rejected by Los Blancos.
According to The Sun, Madrid claimed that Red Devils boss Louis van Gaal was desperate to bring Bale to United and was prepared to smash the current world record fee of £86m that saw the former Tottenham man join Madrid in 2013.
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The publication have claimed sources close to Madrid president Florentino Perez confirmed he refused to do business with the Manchester club.
United deliberately hounded Madrid with bids for the Welsh star, so the Spanish giants would meet their £40m valuation of goalkeeper David de Gea.
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Madrid's reluctance to sell Bale, who was influential in their double winning campaign of 2013-14, is coupled by the 26-year-old's determination to remain at the Bernabeu and turn around his fortunes.
The Southampton academy graduate was the target for angry Madrid fans last season as the club failed to gain any silverware, despite a strong start to the season.
Having scored 22 goals in 44 appearances in his debut season, Bale's influence waned last campaign as he hit 17 in 48 matches, often being made a scapegoat by Real fans looking for a target.
It has recently been revealed that new shirt manufacturer Adidas were keen for Man United to bring the superstar to Old Trafford as their marquee signing of the summer.
The sportswear company were reportedly pushing the Manchester club's top brass to make a world record bid for the player, but following this latest news it is highly unlikely the Madrid club will budge in their stance on Bale.
Van Gaal has been rebuffed in his approach for another Real Madrid player this summer after Sergio Ramos was linked with a move to the club, but is looking likely to sign a new deal at the Bernabeu, however they have not given up hope just yet.
United have also been busy showing players the exit door, with full-back Rafael completing a move to French side Lyon, along with Robin van Persie and Nani leaving the club earlier in the window.
Ed Woodward is keen to flex United's muscles in the window having already made four high profile additions, totalling £80m. Woodward is also close to sealing a deal for Barcelona wide man Pedro.
With Angel di Maria close to sealing a £44m move to PSG, United are keen to strengthen their side further before the window slams shut.