The Crystal Palace winger looks set to leave the club as a free agent later this month after failing to agree a new deal at Selhurst Park.
Zaha has been linked with a move to Saudi Arabia in recent days with Cristiano Ronaldo's Al-Nassr interested in acquiring him.
However, according to Le Parisien, Zaha is giving his priority to European clubs and PSG have made initial contact with the 30-year-old following discussions between relevant parties.
The Ligue 1 champions know they face competition for the Ivorian who has 28 caps to his name.
The report claims PSG sporting advisor Luis Campos has been tracking Zaha for some time and appreciates his ability to be a game changer.
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Campos believes Zaha can add some much-needed energy to the PSG squad - something that has been lacking in recent times.
The Ivorian is one of several options at the Parc des Princes - with Marcus Thuram reportedly close to signing.
PSG have already tied up deals for Manuel Ugarte, Milan Skriniar and Marco Asensio whilst plotting a move for Manchester City's Bernardo Silva who is eyeing a move away from the newly-crowned Champions League winners.
Zaha has spent almost his entire professional career at Crystal Palace after making his breakthrough in 2010
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The winger jumped ship to Manchester United in 2013 but fell down the pecking order under new boss David Moyes before securing a six-month loan to Cardiff.
He was then loaned back to Palace for the 2014/15 season before re-signing permanently at the end of that campaign.