Jamie Vardy is staying at Leicester after snubbing Arsenal to sign a four-year extension, but manager Claudio Ranieri is determined to beef up his goalscoring options nonetheless.
The Italian, who led the Foxes to Premier League glory by 10 points last season, was thought to be interested in signing Watford striker Troy Deeney.
However, The Star have claimed that City have been quoted £30 million for the Englishman, prompting them to identify alternatives.
The report goes on to suggest that Leicester might well make a move for Bony, whom is available for £20 million.
The Ivory Coast marksman has endured a low-profile 18 months at Manchester City following a big-money switch in January 2015, scoring six league goals in 36 appearances for the Sky Blues.
Prior to joining the Etihad Stadium club, Bony had netted over 35 goals in all competitions after spending just one and a half seasons with Swansea City, and Leicester will be hoping to draw that kind of talismanic form from him again.