According to a number of reports in Italy and England, including The Athletic, the Serie A side are putting the finishing touches on a move for the player as they prepare to replace Sandro Tonali, who is set to join Newcastle.
Loftus-Cheek, a Chelsea academy graduate, has spent his entire career with the Blues amassing 155 appearances and scoring 13 goals.
He made 33 appearances across all competitions last season but failed to hold down a regular starting spot.
Loftus-Cheek is set to be one of several Chelsea departures this summer as Mauricio Pochettino looks to mould his squad ahead of the new campaign.
N'Golo Kante and Kalidou Koulibaly already sealed moves to the Saudi Pro League while Edouard Mendy and Hakim Ziyech are also close to exits.
