The Ukraine international is the subject of intense interest from PSG, which have been haggling over a fee with Bournemouth since the end of last season.
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However, with terms yet to be settled, Spurs have now made contact with Bournemouth for Zabarnyi, says talkSPORT.
The Cherries have already rejected a £55m offer from PSG for the defender.
For his part, Zabarnyi is said to want to move to Paris, though Bournemouth are insisting he will only depart on their terms.