The German, a year since leaving Anfield, has agreed to succeed Claudio Ranieri, reports La Stampa.
The Red Bull football chief had agreed a move to another club which was in the middle of changing owners, before committing to the Giallorossi.
Klopp has held talks with the Friedkins, the club owners, and also sports director Florent Ghisolfi, about the need for six new additions, covering the centre-back, right-wing, and centre-forward positions.
Fueling the speculation was a video released by the Friedkin Group, highlighting Roma and it's history.
And in the clip, a sequence of landmarks are shown have the initials that spell out Klopp's name: Coliseum (Kolosseum in German), Lupa (the she-wolf), Olimpico, Saint Peter’s Basilica, and the Pantheon.