This summer, the 30-year-old centre-back joined Roma on loan, triggering a clause in his Leeds contract after the Whites were relegated.
Llorente has played regularly for Roma this season as he has featured 24 times in all competitions for the Italian outfit.
PSG want to bring in a defender and have looked at Llorente, with coach Luis Enrique approving of a move to sign him.
The track appeared to have gone quiet, but according to French outlet Foot Mercato, people close to PSG sporting director Luis Campos held a meeting earlier this week to try to push the swoop forward.
It is suggested that Roma are looking to bring in a centre-back and have no issue with letting the Leeds defender leave.
PSG boss Enrique is said to be an admirer of Llorente and the Spanish tactician believes that the player would fit his squad.
Any move would require Roma and Leeds to both agree, along with Llorente wanting to move to PSG.
