Speculation has linked the 27-year-old with a shock return to his old side just two years after he made the record-breaking move to Paris.
In May, Spanish police carried out an operation against several footballers, ex-players and club executives accused of fixing matches in the first and second divisions, arresting six suspects including former Real Madrid player Raul Bravo.
PSG president Nasser Al-Khelaifi claimed in June that he doesn't want any more "celebrity behaviour" at the club - and said the "doors are open" for any player who doesn't comply.
He has been unable to live up to expectations at Barcelona, but he is impressing at the Copa America with Brazil. The club didn't need to raise the money through player sales but the club wanted to get a return for their unwanted players.
All that remains to be seen is which Barcelona player may be included in the swap.
So far, everything has been handled by a number of intermediaries who are working on the futures of both Neymar and Coutinho.