The Premier League new boys have made a number of bids to sign the 23-year-old so far this summer, none of which have impressed Bruce.
The Tigers boss told the Hull Daily Mail: “Norwich have come in with bids for Robbie but I have to say they have been embarrassing.
“The supporters should know the truth and Norwich came in two weeks ago with a bid of £2million, £2.5million and then £3million.
“That’s ridiculous for someone who is 23, has played two years in the Premier League and has become a regular international.
“When we have just got almost twice that for Tom Ince (who joined Derby for £5million). It doesn’t make sense. We paid £2.75million for Robbie and that was three years ago.
“This can unsettle players and it is all part of the game but Robbie Brady will not be going for anywhere near that.
“If it happens, it happens, but Norwich are nowhere near the figures we would even think about accepting at the moment.”