David De Gea seems to be the most likely transfer target for the goalkeeper position, but Real Madrid are also after Chelsea's Thibaut Courtois, according to François Gallardo. Take this with a grain of salt, as Gallardo has reported a list of at least 20 or 30 players that would be on Real's radar.
Courtois just won the Premier League with Mourinho, and the Portuguese coach will surely refuse to sell the Belgian keeper. Furthermore, Courtois signed a contract extension with Chelsea this year, meaning that his new contract ends in 2019.
Therefore, how much could Chelsea ask for Courtois? He probably is a better goalkeeper than David De Gea, but it would make much more sense for Real Madrid to sign the Spanish instead as his contract with United expires in just 12 months, something that makes the signing much more affordable. The ball is on Iker Casillas' court as well, as the captain doesn't want to leave and make room for a younger, better replacement in the goalkeeper position.