Should he not recover in time then Real would have to field 22-year-old Raphael Varane and the inexperienced Nacho Fernandez in defence.
Ramos dislocated his shoulder against Shakhtar Donetsk in the Champions League and has missed Real's last two games.
“We are looking at the situation with Pepe and he is not ruled out," Real coach Rafa Benitez told a news conference on Friday.
"We will see how he progresses and then we will take a decision whether it is worth risking him or not.
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“Ramos is improving but he is not ready for this game.”
Real missed out on all major trophies last season and Benitez, who replaced Carlo Ancelotti ahead of this campaign, has worked hard on making the defence more secure.
They hold the meanest defensive record in La Liga, with the only goal they have conceded in five games coming against Bilbao.
As well as making the backline more solid, Benitez has ensured the midfield now provide more defensive cover.
The continued development of Varane is another reason for their improvement at the back.
"I already knew about him (Varane) before I arrived and his progress is also down to previous coaches," said Benitez.
"I have coaches and physios who work with him to get the best out of him and along with that is the quality of the player, and the other players in the team."
Benitez’s policy of rotating his squad has so far not included Cristiano Ronaldo and the coach says it is because he is the most valuable player.
“The player who scores the goals is the most important player in a team,” said Benitez.
“We are in a strong position because I know that he will score goals and if he doesn’t then we have James (Rodriguez), (Gareth) Bale, Isco...
“At the moment it is (Karim) Benzema that is on a good run and that is because the team is functioning and giving him passes as well as his quality.”
Real are top of La Liga on goal difference, but tied on 13 points with Celta Vigo and Villarreal.
Barcelona, who were hammered 4-1 by Celta on Wednesday, are a point behind.
(Reporting by Tim Hanlon in Barcelona, editing by Toby Davis)
