Zinedine Zidane wants the United goalkeeper to replace Keylor Navas at the Bernabeu.
Reports have suggested Madrid president Florentino Perez is keen to get a deal done quickly and avoid another drawn out summer transfer saga.
But Manchester United will not let De Gea go for cheap, and are demanding £60million for his services.
Madrid would subsequently have to almost double the world-record fee for a keeper – the £32m Juventus paid for Gianluigi Buffon in 2001.
With Mourinho aiming to bolster his attacking options this summer, Perez is hoping to take advantage.
Madrid’s chief is apparently fully aware Rodriguez is on ex-Bernabeu boss Mourinho’s wishlist.
As the Colombia international is not attracting great and not part of Zidane’s plans for next season, a part exchange could suit all parties.
