Iheanacho is among the players expected to leave Leicester City this summer following the Foxes’ relegation from the Premier League.
Everton, Burnley and Nottingham Forest are among the clubs interested in the Nigeria international.
Besiktas are now leading the race for his signature after establishing contact with Leicester City.
The Black and Whites want to sign Iheanacho on loan, with an option to make the deal permanent.
The 26-year-old was named Leicester City Player of the Season last season.