Manchester United are said to be pushing ahead with a £35million bid for Perisic.
There are claims the Croatia international may have to be sold before 30 June in order for Inter to meet their Financial Fair Play targets.
And PSG believe they may be able to snap up the player before United get their hands on him.
That is according to Italian TV show You Premium Mercato, who claim PSG could agree a swap deal with Inter this summer.
That is because Inter have Lucas Moura on their list of summer targets, claim Gazzetta dello Sport.
PSG are supposedly open to selling Brazilian Moura despite his 19-goal hoard for the side last season.
It is claimed much of the agreement would fall into place but PSG may ask that Perisic becomes part of the transfer.
Premium Sport presenter Daniele Miceli claimed on his TV show YouPremium Mercato that Fiorentina’s Federico Bernardeschi is another target.
Perisic is said to have been on a list of 25 names United manager Jose Mourinho gave to executive vice-chairman Ed Woodward back in March.
Mourinho has already signed Victor Lindelof from Benfica in a £30.8m deal this week.
The club are thought to be pushing ahead with a move for Real Madrid striker Alvaro Morata – although that deal may be delayed as he is getting married on Saturday.
As for Perisic, new Inter manager Luciano Spalletti refused to discuss with his or Mauro Icardi’s futures this week.
“I’ll avoid answering on Mauro and Perisic for now,” he said.
“There are strong players at Inter but they have to get into the team mechanism. It must be the team that works.
“I want all the players who are able to donate something to their team-mates with their quality.”
