The report claims that the talented centre-back will reject a new Burnley contract offer and instead look to force through a move to Claudio Ranieri’s side.
Leicester have been in the market for a new defender this summer as they seek to add competition to regular centre-back duo Robert Huth and skipper Wes Morgan.
With both players in their thirties, Ranieri is looking to freshen things up with a younger player and 23-year-old Keane seemingly fits the bill following his terrific progression at Turf Moor.
The former Manchester United player only joined the Clarets 18 months ago, yet in that time he has stepped up to the plate following Jason Shackell’s departure and helped the club achieve promotion.
Burnley boss Sean Dyche will see him as a key member of his squad ahead of a potential Premier League relegation battle this season, although he could end up losing him before a ball is even kicked.
The report goes on to say that Leicester have already seen a £15 million bid turned down by the Lancashire side, yet Ranieri insists on buying the Englishman and will push harder to acquire his services.
Keane has a contract at Burnley until 2018, and in a previous report by the Mirror he has also been linked with moves to fellow top-flight sides Everton and Stoke City.