Metro reports that PSG are ready to make a £17million bid for the 27-year-old midfielder.
Arsenal boss Arsene Wenger had an opening bid of £10million rejected by the Magpies last week.
Wenger is preparing another bid for Cabaye, but now face stern competition from PSG in the race to sign the midfielder.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.