Anderson, 23, has been one of the league’s breakout stars over the past two season, establishing himself as a regular for Nottingham Forest and England.
Many of the Premier League’s top clubs are interested in signing the midfielder, with Forest expected to demand around £100 million for his services.
According to the Daily Mail, City’s director of football Hugo Viana and manager Pep Guardiola are both big fans of Anderson.
City scouts have attended several Forest games to watch Anderson and are impressed with his game intelligence.
Guardiola’s side aren’t the only ones hoping to sign him, however, with both Man United and Liverpool heavily linked with a move.
