The Nigeria international has seen his playing time limited since the arrival of manager Pep Guardiola last summer, starting just five games in the Premier League - one of those coming in 2017.
Despite his lack of impact this term, The Sun claims that Everton are preparing a shock £20m move for the 20-year-old, who they see as a potential replacement for Chelsea-linked striker Romelu Lukaku.
A City insider is quoted by the publication as saying: "Everton have shown an interest in Kelechi, who has been frustrated with a lack of game time this season.
"He is highly-rated here, but has not started a match since January 2 whereas I'm sure he would get lots of first-team action elsewhere.
"Pep is looking to bolster his ranks and spend a fair chunk of cash this coming transfer window and the club could be persuaded to sell should the right offer come in."
Meanwhile, Sky Sports News reports that West Ham will rival Everton in their pursuit of Iheanacho as they look to bolster their own attacking ranks.