The Spanish giants have endured a turbulent start to the campaign, in the league and in Europe.
A loss to La Liga new boys Cadiz was followed up by a defeat to Shakhtar Donetsk - who had 10 players missing through coronavirus.
Both matches came at the Bernabeu in question marks arose over Zidane's future.
Whether Real would sack the Frenchman is unlikely but the possibility of him walking out has not been ruled out.
Zidane left shortly after winning Real's third Champions League title in a row in 2018 after a clash with club president Florentino Perez.
And if turmoil continues in Madrid, the one-time Ballon d'Or winner could call it a day.
According to El Transistor, Real chiefs have already made contact with Pochettino on potentially taking over should Zidane leave.
The ex-Tottenham boss has long been admired by Perez and has been linked with the post over the years.
With Poch being a free agent, it makes him even more attractive an option as they owe no compensation.
It was only last month where the Argentine admitted managing Real Madrid would be a dream.
He told Marca: "I don't know if I'll ever coach Madrid, but of course it's my dream.
"If it's not the best it's one of the best clubs in the world.
"I'm no different, everyone has it on their dream list."
Manchester United have also been linked with the 48-year-old, should they axe Ole Gunnar Solskjaer.
The Red Devils have also had a difficult start to the season but are backing their manager at the moment.
Real's struggles have been somewhat alleviated after their win over Barcelona in the first El Clasico of the campaign.
It took Los Blancos to second in the league after a 3-1 victory over their arch-nemesis.
Pochettino was sacked from Tottenham last November and has been without a club since.
Jose Mourinho was hired in a whirlwind 24 hour period in north London, who also managed at the Bernabeu.