The England defender's contract at Stamford Bridge expires at the end of the season and so far talks over an extension have failed to find a resolution.
It is believed Chelsea are only prepared to offer the 31-year-old a one-year extension, while Cole would prefer a longer deal.
That has led to speculation the former Arsenal trainee may consider a move away from west London, with big-spending PSG linked with a swoop.
They would certainly have the finances to more than match Cole's wages at the Bridge and his former Gunners team-mate Pires believes he would be the ideal signing for the Ligue 1 club.
The 39-year-old remains friends with Cole and is sure he would be keen on a move to the French capital.
"Paris could be interesting for him, at a sporting level and a financial level," said the former Arsenal, Villarreal and Aston Villa winger.
"He could say okay to Paris. The plans attract him, I know him well and I'm sure he is interested."