The 30-year-old has missed his side's last four matches due to a back problem, but Los Blancos boss Carlo Ancelotti said earlier this week that the stopper was "much better".
Ancelotti revealed that the plan was for the goalkeeper to start training on Thursday in order to be ready for the key La Liga contest with Barcelona this weekend.
"Courtois is much better, the plan is to start training on Thursday and be ready for Sunday. We've talked to him and he's much better," said the Italian ahead of the European clash with Shakhtar Donetsk.
However, Courtois was unable to resume training when planned, and according to Marca, he is now a major doubt for the contest with Xavi's side.
The report claims that it is 'very unlikely' the Belgian will be in the starting side against Barcelona, as he is still in pain with the issue.
Courtois allegedly worked in the gym with a trainer on Thursday, in addition to exercising in the pool, but he was not involved on the grass.
According to journalist Carlos Rodriguez, Real Madrid remain hopeful that the stopper could recover in time, with the club preparing to reevaluate him on Friday.
Courtois has not featured for Los Blancos since the 2-1 win over Atletico Madrid in La Liga on September 18, missing the league clashes with Osasuna and Getafe.
Meanwhile, he was absent for the two Champions League games against Shakhtar Donetsk, with Andriy Lunin enjoying an unexpected run in the team.
Real Madrid will again definitely be without the services of Dani Ceballos on Sunday afternoon due to a hamstring problem, which is likely to keep him out until after the World Cup.
As well as Courtois, Antonio Rudiger is also a doubt due to the head injury that he suffered when scoring his side's leveller against Shakhtar in the Champions League on Tuesday.
Ancelotti will make changes to the side that started the European affair, with Vinicius Junior, Luka Modric, David Alaba, Dani Carvajal and Eder Militao all set to return to the XI.
Real Madrid have won seven and drawn one of their eight league matches this season to collect 22 points, which has left them second in the table behind Barcelona ahead of this weekend's clash.