King is entering the final year of his contract at the King Power Stadium and a number of clubs are thought to be monitoring his situation.
The 25-year-old found himself down the pecking order in Nigel Pearson's starting XI during the second half of last season with Danny Drinkwater and Matty James the preferred central midfield partnership and his suitors are hoping he could be lured away with the prospect of regular first-team football.
The former Chelsea youngster has established himself as one of the best midfielders outside the Premier League in recent seasons and helped Leicester win the Championship title last term.
Watford, Fulham and Wigan are all keen to bring in an attacking midfielder and they see King as someone who could boost their promotions bids next season.
It remains to be seen if Leicester would be willing to cash-in on Wales international King as they prepare for life back in the Premier League.