The publication's senior culture and events editor Marc Malkin also confirmed the news on Twitter, saying the "audience squealed" when Styles appeared onscreen.
In the Marvel comics, Eros is the younger brother of supervillain Thanos (Josh Brolin), who fans will know from the Avengers and Guardians of the Galaxy films.
Eternals – set after the events of Avengers: Endgame – is centered on a group of immortal god-like alien characters who have lived on Earth for 7000 years, secretly protecting humanity from their opposite forces, the Deviants.
It has a star-studded cast, including Angelina Jolie, Kumail Nanjiani, Gemma Chan, Richard Madden, Salma Hayek and Kit Harington.
If reports about Styles' cameo are true, it would make Eternals the former One Direction singer's fourth feature film role since his 2017 debut in the Christopher Nolan-directed war film Dunkirk.
Styles was praised for his acting chops in the critically acclaimed movie, which took people by surprise given his boy band background.
The Adore You singer has managed to go from strength-to-strength since, as he continues to enjoy a successful solo singing career and is also set to star in the upcoming thriller Don't Worry Darling opposite Florence Pugh, as well as a romantic drama, My Policeman, in which he plays a closet gay man.