Zidane faces a crucial 10 days that could decide his future after Real were beaten 2-0 by Shakhtar Donetsk on Tuesday night to leave them in third place in Group B.
Real president Florentino Perez is reluctant to sack Zidane but the 13-time European champions are off the pace in LaLiga after an alarming recent slump.
They must beat Borussia Monchengladbach in Spain next Wednesday to be sure of progress to the last 16 of the Champions League, and also face tough games in LaLiga against Sevilla on Sunday and then Madrid rivals Atletico next weekend.
Zidane has vowed not to resign but, unless results improve, Perez could be forced into a change.
Pochettino, who has been out of work since leaving Tottenham a year ago, is among the candidates being considered by the Real hierarchy.
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