The 27-year-old’s future in Paris has been uncertain all summer but the La Liga club are stepping up their efforts with less than three weeks to go until the European transfer window shuts, reports Sky Sports News.
PSG are unlikely to sanction a sale unless they are able to recoup the £200m they spent on Neymar in 2017, the report claims.
Neymar has been agitating for a return to Spain all summer and told the Ligue 1 champions he wanted to leave in July.
PSG have tried to convince the Brazil international to stay in the French capital but did not include him in the opening-day Ligue 1 win against Nimes on Sunday.
Neymar enjoyed four trophy-laden years in Spain with Barca, winning two league titles, a Champions League and FIFA Club World Cup.
He also won back-to-back Ligue 1 titles with PSG, scoring 51 goals in 56 appearances.