The 24-year-old has been attracting attention from the likes of Leicester City and West Ham United this summer (via Mirror), but Sean Dyche appears to have earmarked the Republic of Ireland international as a target as he prepares his squad for their first campaign back in the top flight, The Irish Sun claims.
Burnley manager Sean Dyche
Though Brady was unable to save the Canaries from relegation last year, he was undoubtedly one of their most impressive players.
He is capable of playing in a variety of positions, especially on the left-hand side, and shone at this summer's European Championships, where he scored two goals to help Martin O'Neill's men reach the knockout stages.
Brady scoring against Italy at Euro 2016
If Dyche is a superstitious man however, he may want to consider that Brady has been relegated from the top flight for the last two seasons, having been a part of the Hull City side that went down in 2015.
And that may be a worrying statistic given that the Clarets have been unable to secure a second successive campaign in the Premier League on the two previous occasions they have been promoted.
However, his performances at Carrow Road last term, as well as in France this summer, arguably prove that he has plenty to offer at the highest level, and his arrival at Turf Moor would certainly be a coup given the reported rivals for his signature.