Bruce has earmarked the recruitment of a striker as a priority following the club-record £12million sale of Republic of Ireland striker Shane Long to Southampton last week.
On Thursday, Blackburn boss Gary Bowyer revealed Hull had made a bid - thought to be in the region of £8m - for Scotland international Rhodes.
And on Saturday morning, the Sky Bet Championship club released a statement on their official website stating their intention of keeping hold of the prolific 24-year-old.
"We have recently received two official bids for the services of Jordan Rhodes from Hull City FC, both have been respectfully and categorically rejected," the statement read.
"The owners of Blackburn Rovers wish to reassure fans that their intention is not to sell Jordan Rhodes as they, along with the manager and board of directors, feel that he is integral to our bid to gain promotion back to the Premier League."
Earlier on Saturday morning, Bruce told Sky Sports News HQ that Hull owner Assem Allam was still in discussions with Blackburn as the club tried to recruit Rhodes, who scored 25 league goals for Rovers last season.
“I knew last night that there were conversations going on between the two clubs. That’s as far as I know really so far,” Bruce said.
“It’s something that we’re trying to progress if that’s possible. It’s always difficult when you’re talking about other people’s players but there has been a bid lodged.
“I believe the first bid was refused but I do believe the two clubs are still talking.”
Bruce also confirmed he was looking to add ‘two or three players’ to his squad before the transfer window closes following a long-term knee injury sustained by new signing Robert Snodgrass.
“In this world of media hype and all the rest of it, it’s very difficult because they usually take weeks these transfers now not just days,” Bruce said. “We need to bring two or three in.
“We know the deadline is 10 days or so away and we need to bring two or three people in at least with what’s happened to Snodgrass and of course Long going the week before.
“Snodgrass is the big one because we lost a top midfielder who gives us the quality that every team needs. He got eight goals in the Premier League for a relegated team so it’s a big blow to us."