Zidane is believed to be losing the trust of Real Madrid's hierarchy, who are doubting his managerial methods this season.
It's thought that the Frenchman's continued rotation of players and opportunities given, or not given, to certain figures are cause for concern.
Club president Florentino Perez is said to have given Zidane his vote of confidence before last week's Clasico.
However, behind closed doors, the situation is supposedly more fragile and Zidane's position is understood to be at risk.
Los Blancos have lost four of their last seven games in all competitions, which is worrying form for a side with such high expectations.
Zidane's crucial second leg matchup against Pep Guardiola's Manchester City side next week could prove a make or break game for the coach.
If Madrid do opt to sack Zidane come summer, they will have a choice between Mauricio Pochettino and Massimiliano Allegri, according to Marca.
As per the report, ex-Tottenham Hotspur boss Pochettino is Real Madrid's first choice to replace Zidane.
It's claimed that the Argentine fits more with the philosophy of the 13-time Champions League winners.
Pochettino is also said to be available to start managing before the summer if needs be.
Meanwhile, Allegri has already said publicly that he will not start coaching again until next season.
"I will not train until next season, I will not do it in any case before," the former Juventus manager claimed.
Pochettino is reported to see the Madrid job as a dream career move and is holding out for an offer, despite interest from PSG who are looking to replace Thomas Tuchel.
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