The 24-year-old is perceived as the perfect successor to Xavi Hernandez, who left Camp Nou at the end of 2014-15, and he's top of Barca's summer transfer target list.
Verratti has become one of the most sought-after central midfielders in the world since signing for the French team in 2012 for an estimated €12 million.
Barca believe they would have to pay around €80m to prise Verratti from the Parc des Princes club, who are adamant they will not sell.
Verratti is believed to be putting pressure on PSG to spend money in the upcoming transfer window to strengthen the best XI and build a squad capable of winning the Champions League.
Chelsea manager Antonio Conte is believed to be a huge admirer of Verratti but the Blues would need to sell Cesc Fabregas to justify the swoop, which they're currently unwilling to do.
Over the weekend, Verratti said he'd be happy to join a Serie A club in the future, however, Juventus' poor working relationship with PSG makes a switch to the Scudetto holders look unlikely.
Real Madrid's interest has cooled off since the departure of Verratti's compatriot Carlo Ancelotti as coach, with Zinedine Zidane already having plenty of central midfield options including Casemiro, Toni Kroos and Luka Modric.
Verratti was accused of partying in the build-up to PSG's humiliating Champions League elimination to Barcelona earlier in March, but he successfully forced L'Equipe into a public apology when he threatened to sue the French media outlet for the claims.
He's featured 32 times for Unai Emery's PSG this season, scoring twice and assisting on six occasions across all competitions.