According to English newspaper, Mirror, Crystal Palace are keen to beat their city rivals West Ham United for the Manchester City forward.
The Hammers are considered frontrunners for the signature of the 20-year-old but Iheanacho is believed to be nursing the ambition of remaining at the Etihad Stadium despite falling in the pecking order of strikers since the arrival of Spanish manager Pep Guardiola.
Iheanacho is one of the players Guardiola is reportedly set to cut loose to create room for new arrivals in this summer transfer window.
However, Manchester City are only ready to sell the Nigerian forward for the right price – a valuation of £20 million.
Everton and Swansea City are also linked with the former Nigeria under-17 star.
Despite limited appearances for Manchester City last season, Iheanacho scored eight goals in all competitions.