The former Real Madrid star has failed to settle in Paris since joining the club in the summer of 2016.
He has scored just one goal in nine Ligue 1 appearances and PSG are resigned to losing him in the near future.
They allowed Jese to join Las Palmas last season on loan but he now appears ready to move to the Serie A outfit.
Fiorentina would have the option to buy Jese at the end of the deal, with PSG set to pay the majority of his wages.
He could complete the move in time to play in Fiorentina's first league game, with Inter Milan coming up on August 20.