The Evening Standard claim that the 20-year-old is the latest player to make the Hammers shortlist ahead of the summer window, with Chelsea’s Michy Batshuayi and Jermain Defoe already considered.
It is understood that Man City are prepared to listen to offers in the region of £20million for their Nigeria international, in order to boost their own summer spree.
The report details that West Ham are considering a bid for the youngster as they look to add pace to their side.
Slaven Bilic need to bolster his attacking options in the summer and is without forwards Andy Carroll, Diafra Sakho and Michail Antonio on Sunday, highlighting a problem they have had for most of the season.
Iheanacho is already a regular for his nation Nigeria and has scored five goals during his eight senior caps so far.
However, the forward has endured a difficult season at the Etihad and fallen down the pecking order under Pep Guardiola.
He has made 28 appearanes across all competitions and scored seven goals in return, but has had to make do with mainly cameo roles in the Premier League.
Iheanacho has found it difficult to force his way into the starting line-up ahead of Gabriel Jesus and Sergio Aguero.
The striker has still made a positive impact during his short career so far and shown his qualities in front of goal, scoring 21 goals in 63 appearanes for Man City.