Cole's current contract at Stamford Bridge expires in the summer, and Blues interim boss Rafa Benitez hinted in an early press conference that he and fellow veteran Frank Lampard are unlikely to be offered new deals.
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This has fuelled speculation of Cole being reunited with former manager Carlo Ancelotti in the French capital, but Leonardo is adamant there has been no contact with the player.
"We have never spoken with Ashley Cole, there has never been any contact," he told reporters.
"Carlo was his coach at Chelsea, that's why that story is doing the rounds."
The Brazilian also dismissed talk of a move for Inter playmaker Wesley Sneijder, who has been exiled from Andrea Stramaccioni's squad for refusing to agree a new deal at a lower wage.
"Sincerely, we have never contacted Wesley Sneijder to come to PSG - we have five players in his position already," he added.