According to Michael van Vaerenbergh, Manuel Pellegrini’s side have set their sights on a potential move for the Nigerian.
Iheanacho’s contract is set to expire at the end of this season, meaning he could be made available for a cut-rate price.
It remains to be seen if that will be the case, or if Leicester City will decide to hold onto him beyond the 1 February deadline.
The striker has contributed five goals and one assist from 19 appearances in the Championship for Enzo Maresca’s side this year.
Betis are seeking a new forward this winter, and have shortlisted three names as their priority targets.
Club Brugge’s Ferran Jutgla is seen as Betis’ first option, with La Liga side hoping to secure an agreement worth €8 million (£6.8 million).
Roma’s Sardar Azmoun is also seen as a potential option for los Verdiblancos if a deal to sign Jutgla doesn’t come to fruition.
Iheanacho has been with the Foxes since making the switch from Manchester City in 2017.
He signed for the Championship side in a deal worth a reported £25 million just a year after their Premier League triumph.