That's according to the London Evening Standard, who report that Chelsea could still make a bid for the striker before the close of the summer transfer window on September 2nd.
Jose Mourinho admitted the recent sale of Romelu Lukaku to Everton for £28m was partly completed to meet Financial Fair Play obligations. And the Blues, despite signing Cesc Fabregas and Diego Costa, are well within the limits having also sold David Luiz and Demba Ba.
The departures of Ashley Cole and Frank Lampard wiped a combined £280,000-a-week off Chelsea's wage bill, which gives Mourinho a significant amount of financial flexibility heading into the final month of the transfer window.
The Chelsea boss insists he has completed his business for the summer, but with money in the pocket and a Premier League title to win, he could be tempted back into the market if the right player becomes available.
And Cavani, who is reportedly unsettled at the Parc des Princes, could be that man. Mourinho is a huge fan of the Uruguayan international, having tried to sign him for £55m this time last year.
A partnership of Cavani and Diego Costa would be one of the most feared in Europe, but the PSG star would command a sizeable salary and Chelsea would need to offload more first-team players to make both the finances and the squad dynamics work.
They would need to sell two non-homegrown players to meet UEFA's quota for the Champions League. The likes of Fernando Torres, John Obi Mikel and Ramires have been linked with moves.
Chelsea defeated Dutch affiliate Vitesse Arnhem 3-1 in a preseason friendly earlier this week, as Mourinho's side continue their preparation for the new season.
£32m recruit Diego Costa has already opened his Chelsea account, and Cesc Fabregas did likewise against the Eredivisie opponents, dispatching a free-kick.