The article adds Neymar has explained he made a mistake in leaving the club, was wrong to want independence from Lionel Messi and has been disappointed by the standard of opposition in Ligue 1.
The 26-year-old has apparently made his desire clear through contact with his former team-mates and with an "SOS" to Camp Nou executives and employees, as well as one un-named director.
A record £198million deal was concluded last summer and those close to the player revealed in the Mundo Deportivo report that the player became blinded by the club's economic wealth.
It was said at the time that, despite the enormous personal financial incentive, it was his ambition to step out of the shadow at Lionel Messi at Camp Nou and prove himself as the best player in the world by winning the long elusive Champions League for PSG.
Another factor that could play a role is that Neymar has been linked with a move to Barca's bitter rivals Los Blancos, and his wish to return to the Blaugrana could be seen as a smokescreen along the lines of "my priority is Barca but if you don't want me, I'll join your bitter rivals".
Asked about the reports on Friday, Valverde said: "It seems to me a fantasy and we do not know where it came from or where it will end".
Having had successful surgery in his homeland, Neymar will be assessed by PSG in six weeks to determine when he will return to training.
Balague told Sky Sports: "We're going to hear in the next few months, even next season, indicating Neymar wants to leave PSG, from different angles". One concerns a return to former club Barcelona and the other details the figure that Real Madrid have been quoted to buy him.
Madrid based newspaper AS also reported that Neymar's father has met Real Madrid's representatives, who are ready to pay €400 Million for the former Barcelona ace.
"I´m not going to talk about a player that is not mine".