Real Madrid are set to invest in a new goalkeeper at the end of the season with Keylor Navas’ future uncertain.
Costa Rica international Navas has helped the club win the Champions League twice in the last three years, as well as the La Liga title.
But Real president Florentino Perez is always chasing the biggest and best names in world football.
And Spanish outlet Diario Gol say the Los Blancos chief is mulling over whether to sign De Gea or Courtois from Manchester United and Chelsea respectively.
Two years ago, Real tried to lure De Gea away from Old Trafford.
A package was agreed with their Premier League rivals, one that would have seen Navas move to England as his replacement.
However, a transfer sensationally collapsed after fax machine problems saw the paperwork failed to be delivered on time.
Ever since, they have spent their time pursuing him but to no avail.
And Diario Gol add they also are keen to sign Courtois from Chelsea.
The Belgium international has become one of the world’s best goalkeepers since returning to Stamford Bridge after a three-year loan spell at Atletico Madrid in 2015.
It has been previously reported that he would be open to the prospect of returning to Spain in order to be closer to his family.
His current contract expires in 2019, and if Chelsea cannot agree a new contract, then Real may opt to sign Courtois instead of De Gea.