The Premier League champions were hoping to land the Republic of Ireland international, but appear set to switch their attention elsewhere.
Norwich's Robbie Brady
The Foxes were hoping to land the 24-year-old as they continue their preparations for a campaign that will see them defend their Premier League title and compete in the Champions League.
However, they now appear set to switch their attention to other targets after deciding that the Canaries' valuation of the Republic of Ireland international is well off the mark.
The Mirror suggests that Leicester's withdrawal from the race may play into West Ham's hands as they are also interested in the former Hull City man. However, the report adds that the Hammers may face an uphill battle trying to convince Brady to join them as he wishes to join a club that offers Champions League football.
Although the versatile wide-man enjoyed a promising season at Carrow Road - and backed that up with some excellent displays at the European Championship - Norwich's asking price is arguably extremely steep.
Though he has impressed lately, the last two seasons have ended with the team he plays for being relegated from the top flight, so it is hardly surprising that Claudio Ranieri is not entirely convinced about parting with such a sum to bring him to the King Power Stadium.
Leicester City manager Claudio Ranieri