Walter Mazzarri currently occupies the manager's position at Inter, having taken charge in May.
However, his long-term future in the role is by no means safe, as the 18-time Italian champions have an infamously impatient board and have employed eight different coaches since 2008.
Vieira, 37, has been put in charge of City's development side this season and many view the Frenchman as the man who will ultimately replace Manuel Pellegrini at the Etihad Stadium.
However, according to The People, City are likely to face a fight from Inter if they want to keep hold of Vieira in the long-term.
Viera has been part of the Man City family since January 2008 when he joined the club as a player, signing on a free transfer from Inter for whom he had made 67 Serie A appearances in three-and-a-half seasons.