The French giants are in the driving seat to sign the England left-back and are ready to offer him a lucrative long-term contract as doubts grow over his Chelsea future.
Cole has failed to agree terms on a new Stamford Bridge agreement, despite having just eight months remaining on his current deal.
The defender, who is set to return to the England team for the World Cup qualifier against Poland on Tuesday night after sitting out the 5-0 win over minnows San Marino on Friday, has been offered only a one-year extension by Chelsea.
Cole, who turns 32 in December, wants at least a two-year deal and is ready to move on if he does not get it.
He is free to negotiate a pre-contract agreement with foreign suitors in January ahead of a summer move, and his west London exit is now looking inevitable.
Sources say the Blues are even willing to offload Cole when the transfer window re-opens if his understudy, Ryan Bertrand, maintains the progress that he has made over the last six months.
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Although he has been playing in a left-midfield role for club and country, Chelsea staff have earmarked him to be Cole's long-term successor at left-back.
PSG are confident that they have the ambition and resources to win Cole's signature. The defender was called "the best left-back in the world" by coach Carlo Ancelotti earlier in October when asked about the club's interest in his former player.
The Ligue 1 outfit have a strong English connection on the backroom staff, where Ancelotti has recruited former Stamford Bridge employees Paul Clement, Claude Makelele and Nick Broad.
Paris' close distance by Eurostar to London could also prove important when negotiations with Cole begin in earnest over the coming weeks.
The breakdown in the full-back's contract talks with Chelsea is believed to be unrelated to the recent controversy over his recent tweet rant against the Football Association (FA).