The European champions are 10 points adrift of reigning champions Barcelona, who have won each of their last seven league games.
With 18 games left to play, the capital club may feel they have plenty of time to get back into contention for the Spanish crown, but history is not on their side.
No team has overcome such a large deficit to go on and win La Liga in the history of the competition.
The most impressive recent fight back from the Santiago Bernabeu outfit came during Fabio Capello's time in charge. In 2006-07, Los Blancos had slipped to six points behind the Camp Nou side after 24 weeks but pulled level with their rivals in mid-May.
The Clasico sides finished the campaign even on points but Madrid's superior head-to-head record saw them confirmed champions.
Before that, it was Barcelona who had made the most impressive comeback. The Catalan side had drifted nine points behind the leaders after 14 weeks of the season in 1998-99 but were able to recover and beat their rivals to the title.
Louis van Gaal's Blaugrana ended up finishing 11 points clear of Madrid that season, but they had more time to bounce back than is available to Solari's team this season.
If Luka Modric and Co. are looking for a successful comeback from week 20 to provide some inspiration, it is Valencia who stand out as the best example.
Under Rafael Benitez's leadership, Los Che were five points behind Real Madrid at this stage of the 2001-02 season but clawed their way back to win the league. They finished an impressive seven points ahead of runners-up Deportivo La Coruna, while Madrid finished a further two behind and Barca came in fourth.