La Liga giants have made it clear that they won't negotiate the sale of the Brazilian international at any price but Marca says that the Catalans could soften their stance if the Ligue 1 side agree to include the Italian midfielder as part of the deal.
Neymar has a €222m (£198m, $262m) release clause in his contract at the Nou Camp after having signed a new deal last summer.
However, PSG would eventually need to pay up to €300m to secure Neymar due to the taxes associated with the paying of release clauses.
Yet, Marca says that the Ligue 1 side could save the taxes if, instead of completing the deal via his buy-out clause, they reach an agreement with Barcelona.
President of the Catalans Josep Maria Bartomeu warned PSG that they would need to pay every penny if they really want to sign Neymar.
"We want Neymar to stay, but release clauses exist. If he wants to leave, they pay the money and he goes," Bartomeu said last week. "They have to pay the value of the release clause, to the very last peseta. Uefa has financial fair play controls and if a club breaks them they are sanctioned. We are the first or second club in the world in terms of income, 800 million euros per year, which allows us to keep growing."
It has emerged in recent days that PSG would be ready to pay Barcelona €222m plus the services of a player like Angel Di Maria or Lucas Moura to convince the Brazil to cash in on the Olympic gold medallist.
However, Marca say that Barcelona believe that it could eventually be an opportunity to make a last-ditch effort to lure top target Verratti.
Nevertheless, earlier in the summer it was well known that the Italian international was the Ernesto Valverde's number one target to bolster the midfield ahead of the coming season.
Barcelona were forced to turn their attention to Liverpool's Philippe Coutinho after PSG refused to negotiate his departure at any price. However, Barcelona's hope could be boosted by the Ligue 1 side's firm desire to make Neymar their marquee signing of the summer.