The LaLiga giants were beaten 2-0 by Shakhtar Donetsk in the Champions League on Tuesday evening.
The result leaves them on the verge of dropping into the Europa League after Christmas.
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It followed defeat by Alaves in LaLiga at the weekend, a result which left them fourth in the Spanish top flight, seven points behind leaders Real Sociedad.
It is now understood that Zidane has just four games to save his job with Pochettino waiting in the wings.
In that period, Real will face Atletico in a Madrid derby and El Clasico against Barcelona.
They also take on Sevilla and Borussia Monchengladbach in the Champions League as they bid to rescue their season.
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