Carvajal has missed the last four games through injury, while Vinicius has been sidelined with a thigh problem since November.
Ancelotti could bring Carvajal into the side for Real Madrid's first match of 2024, but he is likely to adopt a cautious approach with Vinicius, which could see the forward start the game on the bench.
Eduardo Camavinga is also in contention to make the matchday squad after recovering from a knee injury he sustained on international duty with France in November.
Despite receiving an injury boost ahead of Wednesday's home fixture, Los Blancos are still without Thibaut Courtois, Eder Militao, David Alaba and Ferland Mendy.
Ancelotti is set to replace Kepa Arrizabalaga in goal with Ukraine international Andriy Lunin, who has featured in seven league games this season.
While Carvajal could get the nod over Lucas Vazquez at right-back, Fran Garcia is expected to keep his spot on the left side of defence.
With Nacho suspended following his red card in the win over Alaves, Aurelien Tchouameni could be forced to operate as a makeshift centre-back alongside the experienced Antonio Rudiger.
Luka Modric is in line to make a fourth consecutive league start in midfield, where he should be joined by Toni Kroos and Federico Valverde.
Jude Bellingham, who has netted 13 league goals this season, will operate behind a front two which is expected to feature Brahim Diaz and Rodrygo.
Real Madrid possible starting lineup: Arrizabalaga; Carvajal, Rudiger, Tchouameni, Garcia; Kroos, Valverde, Modric, Bellingham; Diaz, Rodrygo