Sport states it hardly took any time for Ernesto Valverde's side to agree a deal of €24m net per season.
There is still much to be done between the two clubs to get the move completed.
But only a year-and-a-half later, Coutinho is already being tipped to depart the Catalan club.
Coutinho arrived from Liverpool in a €142million deal in January 2018, but has struggled to cement his spot in Barca's starting XI.
Former Barcelona player Rivaldo, speaking after playing at Camp Nou alongside supporters as part of a tournament organised by Betfair, says Neymar should never have left the Spanish champions and urged him to return as soon as possible.
"I don't know if Neymar will go to Barcelona because I haven't spoken to him", the full-back said to Cadena Cope.
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Coutinho added: "To play with Neymar is incredible". It's not only me, it's everyone [who thinks that].
As such, the Brazilian player seeks to engineer a move away from the club and return to play alongside Lionel Messi and Luis Suarez - with whom he still maintains a good relationship.
"For me, [Neymar has to leave PSG], because he's a brilliant player who made a mistake by leaving Barcelona", Rivaldo told reporters.
'But I hope it serves me as an example, as a lesson so that I want more, concentrate even more to be able to succeed.
However, some quarters believe the Argentine can not be the "greatest of all time" title following his failure to win silverware for his country at the senior level, as compared to his arch rival, Cristiano Ronaldo, who inspired Portugal to win the 2016 UEFA European Championship in 2016, and three years later won the UEFA Nations League title. Should they turn down the opportunity to land him, then he will consider the option of Real Madrid.