The 'Special One' is currently the manager of Serie A outfit Roma but there have been reports that PSG are ramping up their efforts to snap him up.
An early exit from the Champions League appears to have made up the minds of the Parc des Princes hierarchy on current manager Christophe Galtier, who only took over last summer.
The Frenchman looks set to be axed at the end of the season even though PSG are likely to win the Ligue 1 title as they sit six points clear of the title.
According to RMC Sport, Mourinho has been approached and the two parties are in advanced negotiations for the Portuguese coach to take over.
However, the former Manchester United, Chelsea and Tottenham boss has refuted those claims in classic Jose style.
When asked by Sky Sports Italia about the reports, he said: "If they called, they didn't find me."
With a sly smile, the 60-year-old added: "I've never spoken to them."
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Mourinho was appointed Roma boss in May 2021 and led them to Europa Conference League glory last season, winning the first tournament of its kind.
However, his contract expires in 2024 and there has yet to be talk of a renewed offer.
It had been reported that PSG director Luis Campos has contacted Mourinho over taking over in Paris while his agent Jorge Mendes is in intensive talks.
The French giants could revert back to their big-name policy just a year after trying to go a different direction.
The appointment of Galtier, who led Lille to the Ligue 1 title in 2021, was supposed to signal such a move, with some signings more tuned towards the future.
The acquisitions of Hugo Ekitike, Vitinha and Renato Sanches signalled a change but the impact has not had the desired effect in the Champions League.
For the second season in a row, PSG were knocked out at the first round, this term by Bayern Munich where they were humbled 3-0 on aggregate.
Mourinho, meanwhile, remains one of the biggest names in the managerial world.
Despite taking heavy hits at United and Tottenham, the wily old coach is still a fine tactician, as proved by lifting silverware with Roma after one year in charge.
However, he has not won the Champions League since 2010 when he completed the treble with Inter Milan.
At PSG, that tournament is everything and winning Ligue 1 is not enough to keep your job, as proved by Mauricio Pochettino last season, who was axed after failing to impress in Europe.