The Nigeria international, who has been ruled out of action until February with a torn Achilles, is set to become a free agent at the end of the season.
Bruce confirmed that discussions over extending the 24-year-old's stay at the KC Stadium had taken place, but that the forward had failed to agree terms.
"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," he told The Mirror.
"All contract talks at the minute will be put on the back burner, and we shall concentrate on getting Sone fit."
Aluko has scored once in eight Premier League games this season, with Hull having netted nine in total.
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