The Royal Spanish Football Federation (RFEF) confirmed on Friday that it had postponed the match at Camp Nou because of safety concerns amid the ongoing political tensions and protests in Catalonia.
Violent scenes broke out in Barcelona after nine Catalan political leaders received long prison sentences for their roles in the region's 2017 referendum and subsequent unilateral declaration of independence.
A rally in the city has been called by pro-independence politicians for 26 October, the day Barca was due to host Madrid, prompting the RFEF to intervene.
The Competition Committee has told the two clubs to agree to a revised date for the game before next Monday and Barca suggested 19 December (AEDT) as the best option.
A Madrid statement released early Saturday (AEDT) read: "In light of the Competition Committee ruling which postpones the match scheduled to be played on Saturday 26 October between Barcelona and Real Madrid, and states the clubs must agree a new date for the fixture, Real Madrid wishes to communicate that the date proposed by both said clubs is 18 December [19 December AEDT]."
Speaking earlier, head coach Zinedine Zidane said he was prepared to adapt to any plans to reschedule the fixture.
"If we have to play on the 26th, we will, and if we have to change, the important thing is to be prepared," he said.
"I know there is a lot of debate because it's logical, but my position as coach is this: to be ready on the date that the appropriate person tells us. We'll adapt.
"I have a preference but I'm not going to tell you. We know it could be the seventh, the eighteenth — we'll adapt to this."
The new midweek date, a Wednesday night local time, is seen by many as an appropriate date as neither Barca nor Madrid are involved in the planned Copa del Rey fixtures on the same day.
LaLiga reportedly put forward 8 December (AEDT) as its preferred date, as it would keep the match on a weekend, but this would require Barca's meeting with Real Mallorca and Madrid's game against Espanyol to be moved.
Barca and Madrid are also playing their final UEFA Champions League group games, away to Inter Milan and Club Brugge respectively, within four days after 8 December (AEDT).