Wales international King has enjoyed a superb last year for both club and country and his performances have not gone unnoticed
King was instrumental in helping Leicester reach the Championship play-offs and he impressed in the two semi-final games against Watford.
The 24-year-old, who scored seven goals from midfield this term, is regarded as one of the best midfielders outside the Premier League.
With Leicester having missed out on promotion they could now face a fight to keep hold of the former Chelsea youngster this summer.
The likes of Hull City, Queens Park Rangers, Crystal Palace and Watford are all thought to be monitoring King's situation as they weigh up moves for the player this summer.