The Bianconeri are set to announce a deal for the midfielder in the next 48 hours, according to La Gizzetta della Sport.
According to the Italian publication, the deal would be for €30m.
The news is expected to be announced at a press conference tomorrow.
Florenzi is one of the key figures of the Bianconero side that won Serie A last season, as he has played in all but one game since the beginning of the campaign.
Roma signed him for €20m last summer but he has not featured since then, having been dropped by the club at the start of the season.
La Gazzettas reports that Roma have already signed goalkeeper Alessandro Della Valle, who played alongside Florenza last season.
The move is expected a big boost for the Giallorossi as they prepare for their Champions League Group Stage tie with Juventus on Tuesday.