The Brazilian, who left the Nou Camp in a world record £198million move in 2017, has been unsettled for much of his time in Paris.
Barca failed in their attempts to re-sign Neymar last year, despite offering PSG over £100m plus Ivan Rakitic, Jean-Clair Todibo and Ousmane Dembele.
But the Spanish newspaper claim that the Catalan giants – and Neymar himself – are refusing to give up on a reunion.
The 28-year-old is now said to be openly talking about a move back to LaLiga with his team-mates, telling them that he believes a deal can be done this summer.
Neymar has been in contact with his closest friends in the PSG dressing room, including Kylian Mbappe, during the coronavirus shutdown.
PSG demanded £180m in cash for the former Santos star last summer, but it is believed they will accept closer to £135m now as his contract begins to run down. It expires in 2022.
And it is claimed that Neymar wants to ensure a smooth exit from the Parc des Princes when the transfer window eventually reopens.
PSG have already sealed the Ligue 1 title as a result of the season being curtailed, but the Brazilian is said to have his sights set on winning the Champions League before rejoining Lionel Messi and Co in Spain.