The midfielder could be on his way back to Serie A this winter, with the Artemio Franchi side keen to sign him on a temporary basis
The Viola are desperate to further strengthen their squad in the January transfer window as they aim to qualify for next year's edition of the Champions League, and they see Sissoko as a valuable addition to their midfield.
The 28-year-old joined PSG from Juventus in the summer of 2011, and he has since made over 30 official appearances for the Ligue 1 outfit.
However, the holding midfielder has struggled to secure regular first team action this term, and is therefore keen to move on this winter.
Fiorentina have made it clear that talks with les Parisiens will continue later on Wednesday, and expect to reach an agreement shortly.