Barcelona and Real Madrid have both proposed playing the rearranged El Clasico match on December 18.
The first clash of the season between Barca and Real at the Nou Camp on October 26 was postponed by the Spanish Football Federation (RFEF) on Friday due to the current risk of civil unrest and security fears in Catalonia.
Both Barca and Real were asked set a new date for the fixture and advise the governing body's Competition Committee of their decision by 10am on Monday, 21 October.
The match has been deferred following days of mass protest in Barcelona after nine Catalan political leaders were given lengthy prison sentences for their roles in the 2017 Catalan independence referendum.
Regional police said 16 people had been arrested across Catalonia, while health officials said medical aid was provided to 42 people.
On a fifth day of protests, hundreds of thousands of people waving pro-independence flags and chanting "Freedom for political prisoners" took part in marches across Catalonia on Friday, set to reach Barcelona, the regional capital, later in the day.
Barcelona said in a statement: "On Thursday the club informed the Spanish Football Federation's (RFEF) Competition Committee of its decision to say no to playing the game at the Santiago Bernabeu Stadium, as proposed by the Spanish Football League (LFP).
"The club's desire was to play the Clasico at Camp Nou on the 26th, the date and time previously agreed and the Committee was informed of this in writing.
"The club has the utmost confidence in the civilised and pacifist attitude of its members and fans who always express themselves in exemplary fashion at Camp Nou.
"Nevertheless, having received the decision of the RFEF Competition Committee to postpone the game citing 'exceptional circumstances' and given that it falls to the clubs to agree a new date for the game before Monday, the club will propose December 18.
"The club regrets the inconvenience that this postponement may cause to members, supporters' club members and fans and it has now begun the necessary steps to refund money from Monday, October 21 for tickets already purchased."
Real posted their own statement in which they too suggested December 18 as their preferred date for the rescheduled match.
Real said in a statement on their official website: "Before the resolution of the Competition Committee of the Royal Spanish Football Federation to postpone the game that was to be played on Saturday, October 26 between Barcelona and Real Madrid, and which establishes that the clubs agree on a new date for the same, Real Madrid announces that the date proposed by both clubs is that of December 18."
LaLiga asked the RFEF on Wednesday if the match could be switched from the Nou Camp to Estadio Santiago Bernabeu but both teams rejected this proposal.