Coutinho only joined Barca in January for £142m, but PSG are desperate to keep star player Neymar happy and could look to bring in his Brazil teammate as a result.
Spanish outlet Mundo Deportivo reports that the French champions would be willing to spend as much as £240m on the former Liverpool midfielder and have made Coutinho's agent aware of their interest.
However, an ongoing Financial Fair Play investigation could scupper the deal after PSG also spent big money on Neymar and Kylian Mbappe last summer.
Barcelona would also be reluctant to sell the 26-year-old, who has a £350m release clause in his contract at Camp Nou.
Coutinho scored 10 goals in 22 appearances during the second half of the 2017-18 campaign.