Aston Villa manager Tim Sherwood has revealed in-demand defender Ron Vlaar has told him he wants to stay at the club.
Arsenal manager Arsene Wenger believes squad size is crucial ahead of a potentially busy summer of transfer activity.
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.