The Ukraine defender is a top target for PSG. which first opened talks with the Cherries for the player before the Champions League final.
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The Daily Echo says negotiations have continued, but no price has yet been settled.
Zabarnyi has agreed terms with PSG over a five-year contract - which was settled in that week leading up to the triumphant Champions League final.
Bournemouth have already lost centre-half Dean Huijsen to Real Madrid and are yet to replace the Spain interntional. Zabarnyi's departure would create an even bigger headache for Cherries management as the new season kickoff looms.