Tudor has been in charge of just three games, losing all three, leaving Tottenham just a point outside the Premier League bottom three.
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The Croatian stepped up after the sacking of Thomas Frank, but has failed to turn results around.
As such, the Mirror says the board are considering another change with the team in freefall.
While reluctant to do so, serious discussions are being held about whether to make the drastic change over the coming days.
Tottenham have reportedly sounded out ex-Brighton boss Roberto de Zerbi as their boss for next season, but that is conditioned on them remaining a top flight outfit.