The 24-year-old is out of contract at the end of the season, and now the club are faced with the prospect of losing him for nothing in the summer.
Crystal Palace are one of a number of clubs being strongly linked with Aluko, who joined the Tigers last year from Rangers.
"Sone has turned down our latest offer, which was a very good one, and there won't be any more discussions for the time being," Bruce told the Daily Mirror.
"All contract talks at the minute will be put on the back burner, and we shall concentrate on getting Sone fit."
Aluko, who is currently sidelined with an Achilles injury, has featured eight times for Hull so far this season, scoring once - the winner at Newcastle.