PSG are convinced they will have a deal for Napoli star Khvicha Kvaratskhelia in place by Wednesday.
Despite competition from the Premier League, PSG have stepped forward and already struck terms over a contract with the Georgia star's agent.
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Le Parisien says things are moving quickly and PSG are confident reaching a deal with Napoli inside the next 48 hours.
A fee of around €75m has been mentioned for Kvaratskhelia.
PSG could include a player in their offer to accelerate negotiations and reach agreement before English rivals have the chance to get involved.