Cavani has been strongly linked with the Stamford Bridge side, with some reports even claiming a £7.2m-per-year salary had been agreed between player and club.
But the latest reports from Spain, carried by the Daily Express, suggest PSG are now on the cusp of completing a deal for the Uruguayan international.
The French club will pay Napoli £55m to partner Cavani with Zlatan Ibrahimovic, potentially creating one of the most devastating forward lines in world football.
The striker's proposed salary, reportedly close to £8.5m a season, will make him one of the best paid players in Europe.
The report claims an announcement could come as early as today as PSG put the finishing touches on the deal.
It would end one of the longer transfer sagas of the summer so far. Napoli have continually insisted that they would accept nothing less than Cavani's full £53m release clause.
Real Madrid were also linked at one stage, but appear to have been put off by Napoli's hard-ball negotiating tactics.
All four clubs are among the wealthiest in the world, but PSG looks to be the only one prepared to meet the striker's valuation.