The Premier League newcomers may have to prepare for life without their defender.
The Telegraph have stated that Burnley offered Keane new terms that would have made him one of the highest paid players at the club, but that the 23-year-old would like to talk to the Premier League champions over a move.
Michael Keane of Burnley applauds fans at the end of a game
The defender was a star man for the Clarets in their Championship winning season, and looked likely to be a key figure in Burnley's return to the Premier League.
But the Foxes' interest has thrown his future at Turf Moor into uncertainty.
Though Keane still has two years remaining on his existing contract, the Telegraph say that it is expected Claudio Ranieri's side will return with a new bid for the former England Under-21 defender, meaning an increase on what was reported to be a £15 million offer earlier in the summer.
Burnley's Michael Keane in action with Tottenham's Paulinho (L)
Keane, who made 46 appearances last season and scored five goals, may look to a number of former Manchester United youngsters at the King Power Stadium who experienced title glory last season, none more so than Danny Drinkwater, and fancy his hopes of featuring alongside them in the Champions League in the coming season.
Though Sean Dyche would be hugely reluctant to see Keane leave, a cash sum upwards of £15 million would be superb profit on a player Burnley recruited just 18 months ago at a fraction of that amount, and represent a significant boost to the club's own transfer kitty.
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