The Canaries could lose star man, Alex Neil admits.
Norwich boss Neil
And though Neil insisted the Canaries are not looking to sell Brady this summer, he admitted they will 'look at' offers of a certain price.
"We have had a couple of contacts and different things and asking about his availability but in terms of firm offers then no," Neil told the Eastern Daily Press.
Brady scores against reported suitors West Ham United
"I don’t think anybody is naïve enough to think we need to keep our fingers crossed he stays here. It is going to be a case of if people come in and offer the right money we will have a look at it."
The Scot added: "We are not trying to actively sell Robbie, by any means, and if he was here at the start of the season I would be delighted. Like anything else, every single player has a price, regardless of what club you are at."
Brady, who arrived at Carrow Road from Hull City a year ago, has impressed despite suffering a second consecutive relegation from the Premier League in May.
The 24-year-old continued his fine form for the Republic of Ireland at Euro 2016 - scoring the winner against Italy in Group E - and has been linked with a string of top flight clubs off the back of it.
Brady scores Ireland's winner against Italy
The Sun reported on Sunday that Everton currently lead the race for Brady's signature, after Leicester City, Stoke City, Sunderland, West Bromwich Albion and West Ham all baulked at Norwich's asking price.
The Canaries are said to want £20 million for the former Manchester United trainee, who scored three goals and made another two in last season's Premier League.