PSG are once again looking for a new manager after current incumbent Christophe Galtier has failed to impress. According to reports in France, contact has been made with Mourinho's agent, Jorges Mendes.
It is the second approach for Mourinho made in recent months amid claims former club Chelsea failed in an approach after sacking Graham Potter, with the Portuguese not interested in a third spell at Stamford Bridge.
Mourinho still has one year remaining on his contract with Roma, but has opened the door to an exit this summer.
"I don’t talk to friends, comrades, journalists," Mourinho replied when asked about his future.
"If a few months ago our CEO [Pietro] Berardi said he was sure I would stay, that is his interpretation. If this time Mr. Zazzaroni [a journalist] said what he said is an interpretation of him, I’m not talking to anyone.
"The situation is clear, from a contractual point of view I still have one year on my contract. Football is football, sometimes contracts aren’t the most important thing. "All good, all calm, the next one is always the most important game."
Walter Sabatini, former Roma sporting director, believes there is every chance Mourinho stays up.
He told Sky Sport: "Those who have hired Mourinho know perfectly his behavior. However, it is difficult to say that he wants to leave.
"For now, however, he is achieving results. Of course, it will depend on how the season ends, but Roma have the chance of reaching the final of the Europa League.
"Mourinho has done a great job. Let's not forget the injuries."