The 24-year-old played a key role in the Republic of Ireland reaching the knockout stages of the tournament as it was his goal that won the game against Italy in the group stage.
And he threatened to inspire Martin O'Neill's men to another stunning win as he scored from the penalty spot to give his side the lead against France in the last 16 before the hosts turned the game on its head.
Despite the exit, the Foxes have seemingly decided to cement their interest with a bid for the former Manchester United trainee which would see the Canaries sell the Irishman for the same price with which they bought him one year ago, according to the Mirror.
Though last season was a disappointing one for his current club, Brady's personal form was very impressive, especially considering that he was deployed in several different positions in defence and midfield.
And Claudio Ranieri may be thinking that if Brady is capable of that kind of form when his club and country have gone into most games as underdogs, then he will surely be an excellent addition when joining a team that won the title last year.