Madrid president Florentino Perez is said to be determined to sign a new keeper in the summer despite the impressive form of Keylor Navas at the Bernabeu this term.
The Spanish club made a very public move for De Gea last year but the move collapsed due to late paperwork.
Madrid have drawn up a list of alternatives in the event of missing out on De Gea again and Courtois is top of it.
Courtois is reportedly happy at Stamford Bridge but, with Chelsea likely to miss out on the Champions League next season, he may be tempted to move to a La Liga side.
De Gea has been in superb form for Man United over the course of the campaign and it would be a bitter blow if he was to leave Old Trafford. The hope is that United can fend off Madrid’s advances once again if they do go back in for the Spaniard.