Il Messaggero says the Atalanta coach has held talks with Roma about the job for next season.
Roma coach Claudio Ranieri will step aside this summer and move into a management role.
Gasperini is emerging as a major candidate for the job and talks have been held between the two parties.
It's suggested Gasperini is insisting on SEVEN new additions be made over the summer, with an emphasis on young, hungry players.
The demands would see Roma shed several senior players, with Artem Dovbyk, Paulo Dybala, Mats Hummels, Leandro Paredes and Lorenzo Pellegrini all recommended by Gasperini to be moved on.
Also on Gasperini's agenda to take the job would be a direct line to Roma's owners, the Friedkins, so he can assess how ambitious they are about bringing consistent success to the club.