And the mega-rich Qatari-backed outfit are ready to make it a £40m double deal to take his Manchester United team-mate Nani.
Rooney still has two years left on his current Old Trafford contract.
But PSG president Nasser Al-Khelaifi has made the England hitman, 27, his No 1 target.
He said: “If he wants to be part of the best project in football then there is only one club to sign for.
“I can understand why the owners are interested in Rooney, he is in the top 10 of strikers in Europe.”
PSG are now also keen on Nani, 26, and are set to offer £15m for him.
The Portuguese winger is convinced this will be his last season at United after failing to reach an agreement on a new deal.