Sue Cole, has told Facebook pals: "Well looks like his going somwhere better hear than the talk of man u. Not too far on the Euro star x", before posting a link that intimated he'd already held talks with the Ligue 1 club.
The 31-year-old is in the final year of his contract with the reigning European champions, and has so far yet to agree a new deal to extend his stay in west London.
Blues boss Roberto di Matteo wants to keep the England international at Stamford Bridge, but after Chelsea owner Roman Abramovich implemented a new policy stating all players over the age of 30 will only be offered rolling one-year deals, negotiations between the two parties have reached an impasse.
If PSG win the race for Cole's signature, it will see him reunited with former manager Carlo Ancelotti at Parc des Princes.
The left-back won the Double with the Italian at Chelsea in 2010 and has a strong relationship with his former coach, who has a huge budget at his new Qatari-owned club.
PSG are in a position to offer Cole a lucrative deal to leave the Premier League and end his career in France alongside a host of other big-name players from around Europe.