The Germany international has been a mainstay between the sticks for the Catalan giants since arriving at Camp Nou from Borussia Monchengladbach in 2014.
However, El Nacional reports that Barca will consider the departure of Ter Stegen as they are still keen to reduce their wage bill, amid significant financial concerns at the club.
City are believed to be one of few elite clubs across Europe who would be prepared to match Ter Stegen's €9m-a-year salary, though his potential arrival at the Etihad Stadium would see him competing with current first-choice goalkeeper Ederson.
Ter Stegen, who will see his current contract with Barcelona expire in June 2025, has made 290 appearances across all competitions for the La Liga giants, keeping 117 clean sheets. body check tags ::