The striker was a target for the Foxes back in January but they failed to agree personal terms with the Frenchman.
Leicester reportedly considered signing the 21-year-old again this summer and there was even talk of an £12m bid.
However, Claudio Ranieri decided to look elsewhere and now - according to Sport Mediaset - Milan are ready to end the transfer saga by offering Niang a new contract.
The forward's current deal expires in 2019 and the Italian club are hoping he will agree to a two-year extension.
As well as Niang, Milan are also set to hold contract talks with midfielder Giacomo Bonaventura.