Ríos, 25, is a Colombia international who joined Benfica from Palmeiras last summer for around €18 million and has established himself as one of the most technically accomplished holding midfielders in Portuguese football.
Napoli's emissary attended the victories over Nacional and Sporting CP as well as the most recent fixture against Moreirense, gathering detailed reports on the player.
The Colombian's profile fits what head coach Antonio Conte has previously described as his ideal midfield organiser — aggressive in the press, progressive in possession and strong in the air. Benfica are open to selling but will not negotiate below €35 million.
Roma were interested in Ríos last summer, when Gian Piero Gasperini made him a priority target, and may return for him this summer. Inter Milan, Manchester United and Fulham are also monitoring him.