Coutinho, 26, joined Barca for a reported £142m (R2.5b) from Liverpool in January and is widely expected to become a key figure to the LaLiga champions next season.
But this has not prevented PSG from launching a surprise move via his representatives in a bid to link up Neymar with his international teammate.
Coutinho starred in Brazil's 2018 FIFA World Cup campaign that ended this weekend in the quarter-final and PSG's cheeky move will no doubt strain the relationship between the two club's even further after the highly publicised Neymar debacle in August last year.
According to Mundo Deportivo the Ligue 1 side have already tabled a £238m (R4,2b) bid to the player's agent.
Despite the alleged opening offer, the Selecao star holds a £358m (R6.4b) release clause - which the French side will need to meet in order to begin negotiations with the player.
However, it seems unlikely that Coutinho would be keen on the switch, given his desire to join the Blaugrana saw him force a move to the club seven months ago.