Serie A rivals AC Milan looked to be closing in on a deal to land the Ajax ace ahead of the Premier League duo.
But now, according to the Corriere dello Sport, Roma are also well aware of Bazoer's class and could launch a bid for him in the New Year.
The Stadio Olimpico club are expected to be active in the January transfer window and the 20-year-old Dutchman is high on their list.
The youngster, who has drawn comparisons with Patrick Vieira, has made five appearances in the Dutch top flight so far this season, taking his tally to 51 games since his debut in 2014.