The Hammers have also been linked with Sunderland's Jermain Defoe and also Michy Batshuayi of Chelsea, having failed to secure the Belgian last summer.
West Ham are again without injured forwards Andy Carroll, Diafra Sakho and Michail Antonio for their final Premier League match of the season at Burnley on Sunday.
Boss Slaven Bilic has been short of options up front in a hard season, with Andy Carroll and Diafra Sakho frequently injured.
The Citizens are prepared to listen to offers for Iheanacho to assist them have more funds to do transfer business in the summer, according to Standard Sport.
Nearly all West Ham fans will say signing a new striker needs to be the club's priority this summer but out of the three main linked options - Defoe, Batshuayi and Iheanacho - which would be the right selection?More news: Nevada Becomes Eighth State To Ban Conversion Therapy
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Iheanacho has scored 21 goals in 63 appearances since breaking into City's first team in 2015-16 season, mostly under former manager, Manuel Pelegrini.
The 32-year-old Argentine received an emotional send-off from City fans following their win over West Brom on Tuesday but will now move on - with West Ham plus clubs from Spain and Italy interested in signing the defender.
Having a enjoyed a good partnership at the2013 Federation Internationale de Football Association U17 World Cup in United Arab Emirates, the 21-year-old forward named Iheanacho who was the tournament's most valuable player as the best player he has ever played with.