The two teams are seemingly already in negotiations over signing Neymar with the Parisians reportedly asking for around £270million for the Brazilian.
But Barcelona have now returned with an offer involving Coutinho – who has endured a difficult season at the Nou Camp.
The former Liverpool midfielder copped plentiful criticism from supporters at the Catalan giants for his poor performances over the course of the campaign.
The Brazilian scored just 11 goals in 53 matches in all competitions, including only five in 33 La Liga games.
Philippe Coutinho made the move to Barcelona in January 2018 for a deal worth £105million, possibly rising to £142million.
Manchester United and Liverpool have been linked with swoops for his services, but PSG would now seem more likely to be his next club, especially if Neymar returns to Barcelona.
Meanwhile, Real Madrid will not be making a move for Neymar, according to the same publication, leaving the opportunity clear for Barca to secure the signing of the Brazil international.
However, Liverpool are also believed to be open to the idea of bringing Philippe Coutinho back to the club, according to Le 10 Sport.
The playmaker left Anfield for Barcelona in the winter window of 2018, but has struggled at the club and could head back to England this summer window.
