The 28-year-old Nigerian international, who joined the Foxes from Genk in 2017, had a relegation release clause in his most recent contract.
Ndidi played 300 for Leicester, including 27 times in all competitions this season, but wasn't able to help the club avoid the drop.
Ruud van Nistelrooy's side's fate was sealed with five matches of their season still to play, alongside fellow relegated sides Southampton and Ipswich Town.
According to BBC Football: "Leicester midfielder is available for a £9m relegation release clause this summer.
"The 28-year-old's clause was activated last weekend when the Foxes lost 1-0 to now-champions Liverpool and were relegated to the Championship with five games to go.
"Leicester have since lost 3-0 away at Wolves and the Nigeria international is among several members of the squad now considering his future."
Ndidi is reportedly a target for both Ligue 1 side Marseille and Premier League Everton.
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New Manchester City signing Jeremy Monga claims it was a "no brainer" decision to join the club over Premier League champions Arsenal ahead of the 2026/27 season.
Ipswich Town have bolstered their squad ahead of their Premier League return by completing the signing of Ghana winger Abdul Fatawu from Leicester City.
Chelsea made up for a bad start to overcome Aston Villa 4-1 in the Premier League at Villa Park on Wednesday.
