Norwich's Robbie Brady celebrates scoring their first goal
With Champions League football on offer - and likely improved wages - the Ireland international should be easy to sway.
Brady is currently in action at Euro 2016, which could delay any potential deal.
Republic of Ireland's Robbie Brady in action with Sweden's Sebastian Larsson
The former Manchester United trainee is just 24-years-old and would join ex-Red Devils Danny Simpson and Danny Drinkwater at the club, who played a key role in Leicester stunning the football world by winning the Premier League title this past season.
It is unclear how much he would cost Leicester, but Norwich would be keen to recoup the £7 million they paid to sign Brady from Hull City a year ago.
Republic of Ireland's Wes Hoolahan celebrates after scoring their first goal with Robbie Brady
The winger has suffered two consecutive relegations, but at Leicester would hope to be taking on a very different challenge at the top end of the table.
Last season he scored three goals and provided two assists for Norwich, and improvement on 2014/15 where he failed to net at all, creating two goals.
Norwich's Robbie Brady in action with Arsenal's Hector Bellerin