The 20-year-old Nigerian is in advanced talks with the Foxes and is thought to be keen to make the switch.
Iheanacho has scored 21 goals in 64 games in all competitions since making his debut for Manchester City in 2015.
Last August, he signed a new contract until 2021, but saw his playing time limited by the January arrival of Brazil forward Gabriel Jesus.
Manchester City striker Kelechi Iheanacho is close to making a £25m move to Leicester City.