RFEF confirmed the postponement of the match last Friday after political unrest in Catalonia.
Violent scenes have broken out in Barcelona after nine Catalan political leaders received long prison sentences for their roles in the region's 2017 referendum and subsequent declaration of independence last Monday.
A rally in Barcelona has been called by pro-independence politicians for October 26, ultimately resulting in El Clasico's postponement for security reasons.
RFEF left Barca and Madrid to agree a date between themselves and they mutually accepted to reschedule the match for December 18, but that now looks unlikely.
LaLiga is reported to have insisted on the game being played on December 4 and RFEF has passed its comments on to the clubs, who have been given until 20:00CET Tuesday to respond.
RFEF's statement read: "The Competition Committee of the Royal Spanish Football Federation will return to Barcelona and Real Madrid tomorrow [Tuesday] after receiving new statements from the National Professional Football League [LaLiga] on the date of the Clasico [originally] to be played on October 26 and was postponed due to exceptional circumstances.
"The clubs will have a deadline to answer by 20:00 on Tuesday, and the Competition Committee must meet again to assess their responses.
"During the day, the Competition Committee has analysed the proposals of both clubs, which it invited to agree to a day and who have agreed to play the postponed match on December 18.
"It [the Competition Committee] has also analysed the various reports sent by the National Professional Football League during these days.
"In addition, the Committee requested a report from the RFEF Competition Area, which has been sent to them in a timely manner."