The Nigerian is said to be a target of a number of Premier League clubs - including Leicester City and West Ham United - but it has now been claimed that the Saints have identified the 20-year-old as the player to strengthen their attacking department.
According to The Sun, that has also thrown up the possibility of a swap deal involving Iheanacho and Southampton defender Ryan Bertrand.
City boss Pep Guardiola is in the market for full-backs and has already been linked with a move for the England international, who could be looking to leave St Mary's this summer.
Guardiola has also been linked with a number of other players who can play at both right-back and left-back, but he could be tempted to offset the cost of the 27-year-old by offering Iheanacho in exchange.
The forward has an impressive scoring record at the Etihad Stadium, but he made a total of just six starts in the Premier League and Champions League last season.