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.
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.
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.
"I will not train until next season, I will not do it in any case before," the former Juventus manager claimed.
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