Marca says that David De Gea also remains on Los Blancos' agenda but the Spain international "could be motivated" to extend his stay at Manchester United having also received an offer to renew his current contract at Old Trafford.
The goalkeepers of Chelsea and Manchester United have both been heavily linked with a move to Real Madrid, speculation that returned last season after Keylor Navas endured a shaky start to the campaign.
But Los Blancos eventually decided against signing a new number one in the summer with the Costa Rica international recovering his best form in the season run-in, helping Real Madrid to clinch both the La Liga title and the Champions League crown.
However, Keylor Navas is already 30 and Marca suggests that Real Madrid are still monitoring the situations of a number of world class goalkeepers ahead of making a future move.
Athletic Club Bilbao youngster Kepa Arrizabalaga and AC Milan starlet Gianluigi Donnarumma have also been named as potential alternatives in recent months but Marca now suggests that the main two options are still Courtois and De Gea.
Marca also mentions Jan Oblak, but they believe that his move from Atletico Madrid to Los Colchoneros' neighbours is unlikely due to his loyalty to Diego Simeone's side. Reports also suggest that Paris Saint-Germain could meet his €100m release clause to lure him to Ligue 1.
Courtois, 25, has been on the radar of Real Madrid since impressing in La Liga during a three-season loan stint at Atletico Madrid.
In June, Courtois' agent Christophe Henrotay revealed that Real Madrid have retained an interest in the Chelsea keeper and that he is in regular contact with officials from the Spanish champions.
"Of course Thibaut is of interest to the big clubs, including the last Champions League winners," Henrotay told Belgium's Sport Magazine. "He is someone who helps you makes you win games and titles. I regularly meet the directors of Real Madrid and of course, Thibaut's case has come up. It is my role to keep him updated on the situation."
Marca says Courtois has also not given up on the idea of returning to La Liga and a move to Real Madrid could make sense for both parties.
Courtouis has publicly stated that he is happy at the Premier League champions, but Marca claim that he believes his time at Stamford Bridge may be coming to an end.
The Spanish publication says he has therefore decided to put contract talks on hold, with his current deal set to expire in 2019.
Roman Abramovich is said to making every effort to tie him down to a new deal but, if Courtois doesn't sign a new deal, the Blues will need to decide whether to cash in on with him at the end of the season - or risk letting him go for free the following summer.
Marca doesn't say when Real Madrid plan to make the move but they add that 25-year-old Courtois would come in as a long-term replacement for Navas.
Manchester United number one De Gea has also been linked with Real Madrid since his proposed move to Los Blancos collapsed in the summer of 2015 after paperwork failed to arrive at La Liga headquarters on time.
The Spaniard's current contract at Old Trafford will also expire in the summer of 2019.
However, Marca provides much better news for United fans as they say that De Gea looks motivated to sign a new deal at Old Trafford given the project currently in place at Jose Mourinho's side.