The Independent says Sterling is a name the club's analytics department 'have been working on' as they settle on their summer targets.
At this stage, Jadon Sancho is the priority.
United, supposedly, 'will do anything' to get the Borussia Dortmund star, who has been in electric form over at the Westfalenstadion this season.
But the report suggests the Red Devils are interested in signing Sterling from their fierce rivals, with the player's future at the Etihad uncertain.
As things stand City are banned from playing in the Champions League for the next two years.
They have, however, appealed UEFA's punishment - which was for breaching financial fair play regulations.
If City are unsuccessful, though, United will reportedly go after Sterling with the club convinced he'd be a shrewd signing.