The Times says Chelsea will hold a review of Pochettino's position at the end of the season and there is no guarantee of him holding on.
And as the campaign runs down, the board has a three man list of alternatives.
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Sporting CP coach Ruben Amorim features prominently, with free agent Hansi Flick and Brighton boss Roberto de Zerbi also being discussed.
Flick has been available since leaving the Germany post last year. He was under consideration at Barcelona before Xavi recommitted last week.