Wijnaldum will be out of contract at Liverpool at the end of this month and is set to leave the club at the end of the season.
The Dutchman has long been linked with a move to Barcelona and his representatives held talks with the Catalan giants recently.
Barcelona were largely considered the favourites to sign him but PSG have moved ahead in the race to land the midfielder this summer.
There were suggestions that PSG have put forward eye-watering sums for Wijnaldum, which was claimed to be double the wage offer that Barcelona made, but according to French sports daily L’Equipe, that is not the case.
PSG have made an offer which is above the €5.5m per season Wijnaldum earns at Liverpool and is claimed to be substantial.
The Ligue 1 runners-up believe that they have offered a competitive salary and talks between the player and the club have been progressing.
Wijnaldum is tipped to move to the Parc des Princes, but no agreement has yet been signed between the club and player.