The Liverpool playmaker signed a five-year contract to stay at Anfield in the February of last year and the club have stood firm against interest from other clubs in the past.
However, according to Le 10 Sport, their resolve will be tested again this summer by the Ligue 1 champions.
PSG are believed to have approached Coutinho’s representatives to discuss a potential move but a formal offer is yet to be made.
The Brazil international is currently away with his country as they prepare for the Copa America and their opening game of the tournament against Ecuador on Sunday.
Liverpool will be keen to keep hold of Coutinho having seen Luis Suarez and Raheem Sterling leave the club in each of the last two summers.
The former Internazionale player is known to want Champions League football, though his agent, Kia Joorabchin, has previously insisted that his client in happy on Merseyside.
Coutinho scored 12 goals in 43 appearances last season and was instrumental in Liverpool’s run to the Europa League final, which ultimately ended in defeat to Sevilla.
The 23-year-old picked up a clean sweep of awards at the club's annual ceremony, picking up both the 'Player of the Year' and 'Players' Player of the Year' gongs.
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