Blackburn Rovers striker Rhodes has emerged as a top target for Hull as they seek added firepower.
An initial approach from the KC Stadium has been knocked back, with it reported that a £12million offer has been rejected.
Bruce is refusing to give up the chase, though, as proven goalscorers are hard to come by.
He says another round of talks are planned, after which he will either push ahead to bring Rhodes on board or turn his attention to other striking talents.
Bruce said in the Hull Daily Mail: “It’s difficult. We got an indication from Blackburn 2-3 days ago, or a week ago, that they were prepared to sell. But now we hear he’s not for sale at any price.
“We’ll have a conversation with Blackburn in the next 24-48 hours then if it’s not to be, we’ll go for the next one.
“Is he for sale or is he not for sale?”