Newspaper L'Equipe and radio station FranceInfo claimed the Frenchman had agreed to update Mauricio Pochettino at Parc de Princes.
A source close to the membership informed AFP later that "severa discussions are underway", no matter the reviews.
Argentinian Pochettino, who become appointed in January remaining year and led the membership to the Ligue 1 title within the season simply ended, has every other 365 days ultimate on his agreement.
French newspaper have mentioned but that Pochettino and the membership to come back to an agreement that might see the Argentine leave the French capital.
Galtier's current employers had been unavailable for comment.
If he does make the flow to Paris, Galtier might reunite with Louis Campos, PSG's these days appointed football consultant.
Earlier this month, French press linked former Real Madrid boss Zinedine Zidane with the location, with PSG's Qatari owners determined to win the Champions League.
France World Cup winner Kylian Mbappe signed a brand new cope with the Parisians last month, deciding on towards joining the Spanish giants.
The new French pinnacle-flight season begins at the weekend of August 6-7.
A week before that, champions PSG will play French Cup winners Nantes in the Trophee des Champions, the traditional curtain-raiser to the French season, in Tel-Aviv, Israel.
