The pair have been absent with respective knee and head injuries, and Real head coach Carlo Ancelotti confirmed the pair are not ready to return for the semi-final clash with the Mexican side in Marrakech.
However, Ancelotti was more optimistic that forward Rodriguez and midfielder Khedira will be fit for Real's next match - which could be Saturday's final.
"James and Khedira will not be available for the game tomorrow," the Italian said.
"But they definitely will be for the next game."
Ancelotti brought great success to the Santiago Bernabeu in his first season in charge by clinching a Copa del Rey and UEFA Champions League double.
And he is now urging Real, who are on a 20-match winning run, to finish 2015 in style by adding another trophy to their collection.
"Every team here is a champion, so for us to win this competition would make it unforgettable," Ancelotti added.
"Cruz Azul have quality, they have players with experience. I think it will be an intense game, they play good football."
Ancelotti also insisted there was no problem with centre-back Sergio Ramos amid rumours of a delay in contract talks.
"The club wants to renew Ramos' contract," he continued. "Ramos wants to stay so there's no problem."
