Mahrez has made clear his desire to leave the King Power Stadium in this transfer window, having shunned reported interest from Barcelona and Arsenal to help Leicester in their maiden Champions League campaign, in which they reached the quarter-finals.
Leicester boss Craig Shakespeare claimed on Tuesday that the club was yet to field a bid for the winger, who scored just six Premier League goals last term, having hit 17 the previous campaign to fire the Foxes to the most remarkable of title triumphs.
"Riyad Mahrez is definitely a great and interesting player," De Francesco said.
"[He is] one of those who maybe Roma is following. A left-footer playing on the right-hand side, which could be of great help to the team."
Roma have been busy in the transfer market since hiring Di Francesco, with new sporting director Monchi making his mark with nine permanent signings, including Hector Moreno, Rick Karsdorp and bringing Lorenzo Pellegrini back to the Stadio Olimpico.