Equipe, whose reliability doesn't appear to be as strong as it once was, make the claim that a €25m bid has been knocked back but that Everton are now prepared to accept between €30m and €35m, down from €40m.
The Liverpool Echo report, however, that Everton have still not received a bid for Gueye and that PSG have been informed that he is not for sale.
The talk comes amid continued speculation across the Channel that Gueye has already been in talks with the Parisian giants and has broadly agreed personal terms should the two clubs come to an agreement.
Gueye, who was signed by Ronald Koeman in 2016 and has 83 Premier League appearances under his belt for the Blues, turns 30 later this year.
Whether or not there was any truth in this original report, it was been followed today (Sunday) by another from Sky Sports via FMC that Everton have knocked back a £21.5m offer from PSG for Gueye.