After having a £15m bid for the Uruguayan turned down in January, the 'foxes' were expected to return with another bid for the player this summer following Middlesbrough's relegation.
However, according to 'The Daily Star', that will not be the case. The paper reports that Middlesbrough have offered the 26-year-old to Craig Shakespeare's side for a knock-down price of £10m but Leicester have rejected the proposal and have instead set their sights on Swansea's Gylfi Sigurdsson.
Ramirez's behaviour frustrated the club hierarchy at Middlesbrough last season, with the player submitting a transfer request just six months after signing permanently for the side that re-launched the player's career.
Local source 'The Northern Echo' reports that Ramirez has no future at the club and that there will be no fresh start for the player this sumer, despite the arrival of new manager Garry Monk.