Stoke City chairman Peter Coates says the club are determined to keep hold of goalkeeper Asmir Begovic this summer.
Manchester City defender Aleksandar Kolarov wants to return to Italy to play in Serie A.
Cole has been linked with a move to the big-spending Parisians since Carlo Ancelotti - the former Chelsea boss - took over the Ligue 1 side.
But PSG's sporting director Leonardo insists there was no truth to reports that the England left-back or Inter Milan midfielder Wesley Sneijder are on the way to France.
"We have never spoken with Ashley Cole, there has never been any contact," he said.
"Carlo was his coach at Chelsea, that's why that story is doing the rounds.
"Sincerely, we have never contacted Wesley Sneijder to come to PSG - we have five players in his position already."
PSG, the French league leaders, are currently in Qatar with Ligue 1 on a winter break.