The Barcelona superstar is closing in on a blockbuster move to the Ligue 1 giants, who are prepared to activate his £199m (€222m) release clause.
Coutinho, 25, has emerged as a major target for Barca this summer.
Liverpool have already rejected a bid worth £72m for their star man.
But, according to reports in Spain, the Reds could soon be forced to fend off interest from big-spending PSG.
Neymar has been talking to Coutinho about a potential move to the French capital club.
Sport claim he has been bombarding his pal with WhatsApp messages, telling him to snub Barcelona for PSG.
As part of his own move to PSG, the club's chiefs asked Neymar for a list of players to sign.
Coutinho, who has been friends with the Brazilian icon since the age of 14, was reportedly high on the list.
The Liverpool star had originally been targeted by Barcelona in a bid to keep Neymar happy.
But Nou Camp chiefs now see him as a priority signing, despite Neymar's imminent departure.
Meanwhile, Jamie Carragher has tipped Coutinho to stay at Anfield for one more season.
"Hopefully we can get 12 more months out of him," Carragher said.
"When he signed his five-year deal, I didn't think that he would see it out.
"There is no doubt that at one stage in his career Philippe will want to play for one of the Spanish giants as many of the South American players do."
