Leicester's relegation to a lower division has triggered a clause in Ndidi's contract, allowing him to leave the club for a set fee of £9 million this month.
United had previously explored the possibility of signing Ndidi last year, but he eventually signed a new three-year contract with Leicester in July.
Ndidi, a 28-year-old Nigerian international, has been with Leicester since 2017, when he joined from Genk.