According to the Leicester Mercury, the Foxes will look to move King on in the next transfer window and have decided the midfielder is no longer of use to the club going forward, despite being the longest-serving player in the current side.
King has spent his entire career with the club, having joined Leicester's youth setup from Chelsea in 2006. He was the first player in the Premier League era to achieve the feat of winning the top three divisions of English football, having ascended from League One to Premier League champions with the club.
The midfielder spent the second half of the 2017/18 season on loan at Swansea, making 11 league appearances but was unable to prevent the Swans from suffering relegation at the end of the campaign.
King is also a seasoned Wales international and was a member of Chris Coleman's squad for the 2016 European Championships, in which the Dragons famously battled to reach the quarter-finals of the competition in their first major tournament since 1976.
Though he has been a loyal servant to Leicester, the club and Puel clearly believe King's best years are behind him and the 29-year-old is unlikely to feature for the club going forward.
Meanwhile, King's Leicester teammate and fellow Premier League title winner Danny Simpson has been included in the club's squad for the league, despite also being yet to feature in a game for the Foxes this season.