The 20-year-old Italy midfielder signed a five-year contract at the Parc des Princes when leaving Pescara last August and he played a key role as PSG won the Ligue 1 title.
His performances for club and country have now alerted a host of European rivals and, with Serie A club Napoli investing heavily in the transfer window after selling Edinson Cavani to PSG for 64million euros, the French capital club have moved to secure their young playmaker's services.
Verratti's agent Donato Di Campli told the Gazzetta dello Sport: "We are still a long way from an agreement. The talks must continue, I'm not too confident or optimistic at the moment.
"Yet Marco will stay at Paris Saint-Germain because he has a four-year contract - that is a fact.
"However, there are alternatives out there and just this morning a monstrous offer arrived from (Napoli president Aurelio) Di Laurentiis.
"Marco wants to be recognised as the great player he is, but what was said (in negotiations) this morning wasn't good, and so we will speak again next week.
"We will speak to Marco and his family, then we will decide."
Under new head coach Rafael Benitez, Napoli have made concerted moves to challenge Juventus's dominance on the peninsula, first signing winger Dries Mertens from PSV Eindhoven and then Real Madrid duo Raul Albiol and Jose Callejon.
Furthermore, the Azzurri are expected to complete a season-long loan deal for Liverpool goalkeeper Jose Reina and a 40million euro move for Real striker Gonzalo Higuain later on Thursday.
PSG general manager Jean-Claude Blanc remains confident Verratti will honour his contract and ignore Napoli's overtures, but he would expect the Parisian club to be rewarded with matchwinning performances in return.
"He's our player, he's under contract for four years," Blanc said. "We are talking about things and I'm confident.
"We want to show Marco how we hold him in high esteem but we also want him to show more of the quality he's already demonstrated."