Both players' contracts are up at the end of the campaign and Messi is yet to commit to a new deal with Barca after trying to force an exit last summer.
Madrid and their coach head to Camp Nou under pressure after consecutive defeats to Cadiz in La Liga and Shakhtar Donetsk in the Champions League.
Barca have lacked purpose and clarity in recent months and three defeats in the league is already more than they endured in the entirety of their title-winning run last term.
The draw left champions Barca top on 36 points after 17 games with Real also on 36, five clear of third-placed Sevilla.
The fixture had to be postponed in October due to violent demonstrations and there are renewed fears of unrest breaking out around Camp Nou, where Barca and Madrid will tussle for the top spot in La Liga.
The fixture was originally scheduled for 26 October but had to be postponed and there are renewed fears of unrest at Camp Nou, where Madrid and Barca will be playing for first place in La Liga.
The clubs have until 10 am (0800 GMT) on Monday to find a new date for the match originally scheduled for 26 October, the federation said.
Luka Modric and Gareth Bale each did gym work indoors as they attempted to recover from injuries sustained playing in the Euro 2020 qualifier between Croatia and Wales on Sunday.
The two clubs will meet twice in four days at the Santiago Bernabeu in a battle of first against third in La Liga.
Cristiano Ronaldo, with 451 goals in 438 games in all competitions, was Real’s all-time top scorer before he left to join Serie A’s Juventus during the close season.
With Messi injured and Ronaldo departed to Juventus, both Barcelona and Real Madrid will need new heroes to emerge when they meet in El Clasico on Sunday.
The former Spain manager had insisted he felt able to continue at the helm in Madrid yet could still not give any guarantees that he would remain in charge by the weekend.
Champions Barca have 87 points while Real are third in the Liga standings with 72 after 35 games.
Atletico Madrid are second on 75 points, 11 behind champions Barcelona who have two games in hand.
Barcelona wrapped up the title last weekend and face European champions Real on Sunday.
Barca are nine points clear of nearest challengers Atletico Madrid at the top of the standings.
It is a scenario few could have foreseen after Real won a Liga and Champions League double last term and began this season so convincingly.
The match marks just the second time, and first in 35 years, that El Clasico will be played outside Spain.
