The France international has not featured for Los Blancos since El Clasico at the end of October, having suffered a fractured foot, missing his side's last five La Liga matches.
Tchouameni was also absent for Real Madrid's last three Champions League Group C matches against Braga, Napoli and Union Berlin.
Initially, it had been thought that the midfielder would be missing until at least January due to the nature of the damage, but according to journalist Carlos Rodriguez, the midfielder is set to be available for Sunday's La Liga clash with Villarreal.
Tchouameni is expected to train with Real Madrid on Friday, and Rodriguez has claimed that he will then be named in the squad for his side's penultimate match of 2023.
Los Blancos are believed to have been shocked by the midfielder's rapid recovery, although he is not expected to start on Sunday, with his return potentially coming off the bench.
Dani Carvajal is also said to have made excellent progress in his recovery from a calf problem, with the Spain international potentially being available for the clash with Alaves on December 21.
Vinicius Junior, Eduardo Camavinga, Eder Militao and Thibaut Courtois are all out for Los Blancos until next year, but Arda Guler is said to be in the latter stages of his recovery from a muscular problem.
Guler is still waiting to make his debut for Carlo Ancelotti's side, having suffered three separate injury problems since he made the move to the club over the summer.
Real Madrid will enter their clash with Villarreal off the back of a 3-2 victory over Union Berlin in their final Champions League group-stage fixture on Tuesday night.
The capital side were held to a 1-1 draw by Real Betis in the league last weekend, though, and they currently sit second in the table, two points behind the leaders Girona.
Real Madrid will end 2023 with a trip to Alaves, with their first match of 2024 then taking place against Mallorca on January 3.
There remains speculation surrounding the future of head coach Ancelotti, with his contract at Bernabeu due to expire next June.
Brazil are keen to appoint the Italian as their new manager, but there have been suggestions that the 64-year-old could sign a new contract with the Madrid giants.