The BBC and The Telegraph have both reported that Manchester City have accepted the Foxes' £25million bid for the Nigerian forward.
The 20-year-old is apparently keen on switching to the King Power Stadium and has already agreed personal terms with the former Premier League champions.
The youngster is currently on holiday but will return over the next few days to complete a medical in the East Midlands.
The reports over the past few days have suggested that Craig Shakespeare is now in pole position to land the Nigerian's signature as a result of Slaven Bilić's West Ham United dropping out of the race.
Various European clubs were credited with an interest in acquiring the services of Iheanacho ahead of the 2017-18 season.
Despite this, Leicester are now clear favourites to sign the youngster having met Manchester City's asking price in recent days. It is suggested that the Foxes are increasingly confident that Iheanacho will become a Leicester City player this month.
Striker's impressive statistics
The young starlet burst onto the scene during the 2015-16 campaign as he scored 14 goals in only 35 appearances in all competitions - including the winner on only his second game for the club against Crystal Palace.
This record is all the more impressive considering he was only included in the starting line-up on 11 occasions.
His goal-haul the following campaign was slightly less eye-catching but he still scored seven times in only nine starts - making a further 20 appearances from the substitutes' bench.
Down the pecking order
Despite Iheanacho possessing one of the most lethal strike rates in Premier League history, he has found opportunities at the Etihad Stadium hard to come by.
Sergio Agüero is the key man under Pep Guardiola and the arrival of Gabriel Jesus in January limited Iheanacho to only one Premier League start in 2017.
If the forward moves to the King Power Stadium, he will face competition from the likes of Jamie Vardy, Islam Slimani, Shinji Okazaki, Leonardo Ulloa and even Ahmed Musa.