Arsenal have been heavily linked with the former Atletico Madrid midfielder who has struggled for game time this season.
The Turkish International only played 18 La Liga games this term and reportedly wants a move away from the Club for regular football.
Turan moved to Barcelona from Atletico Madrid during Barcelona's transfer ban in 2015 and had to sit out from football for six months.
However, since his inclusion, he failed to meet the expectation and often found himself out the team.
Arsene Wenger has been linked with Turan in the past and is considered to be willing to offer him an exit route from Barcelona this summer.
And if some of the reports are to be believed fellow countryman Lionel Messi is keen to line up Di Maria as his probable replacement.
The Barcelona board believes that Leo Messi will be able to persuade his Argentina teammate to move to Catalunya and help new head coach Ernesto Valverde to make his side ready for the La Liga title once again next season after losing out against Real this season.
He signed for PSG for a reported £44m in 2015 and has two years remaining on his current contract with Les Parisiens.
The Winger only scored 14 goals and provided eight assists in all competitions this season as PSG lost out to Monaco in the league as well suffered a huge 6-1 defeat against Barcelona in UCL to crash out of the competition. Although he helped his team in winning the Coupe de France and Coupe de la Ligue.
The 29-year-old spent four years at Madrid between 2010 and 2014, winning a La Liga title, two Copa del Reys, and a Champions League, before joining PSG from Manchester United.
So should the transfer occur, Madrid fans will surely get a blow to see their former attacker turn out for their arch rivals after his successful four-year spell at the Bernabeu.