Having announced the dismissal of caretaker manager Igor Tudor on Sunday, Spurs are now attempting to convince De Zerbi to take the job long-term.
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De Zerbi, who is available after leaving Olympique Marseille last month, had planned to sit out the remainder of this season before assessing job offers.
BBC Sport says Spurs are hoping to convince the Italian to take the job immediately, with the team sitting just one point above the dropzone.
Spurs were in contact with De Zerbi to ascertain whether he was interested before taking the decision to part ways with Tudor.
However, it remains to be seen if the former Brighton manager can be convinced to take the post now.