Reports over the weekend suggested that Fulham were planning to remove Kit Symons and attempt to lure Bruce to Craven Cottage with the promise of transfer funds.
However, Bruce - who was also linked with Fulham before Symons took over permanently last October - claims the rumours are disrespectful.
"I was getting the sack [according to reports] the day before and then Fulham want me," he said.
"Unfortunately, the media today, I can't do anything about it. The unfortunate thing is there's a manager in situ at Fulham and I have respect for Kit Symons.
"I can't comment as it just fuels it. It's rubbish journalism."
Bruce saw his side come agonisingly close to beating champions Manchester City on Saturday, before James Milner scored a sublime injury-time free-kick to salvage a 1-1 draw.
The former Sunderland manager is hoping Hull - who are 18th - can take heart from that performance into Tuesday's encounter with Aston Villa – two points and two places above them.
"You hope it gives us a bit of confidence because after the run we've had and the disappointments we've had you want that confidence," he added.
"We were a minute from beating them. It's a big game tomorrow, what happened at the weekend is gone, let's hope it gives us that belief."
Bruce also confirmed that January signing Dame N'Doye may make his debut against Villa, adding: "He's in our thoughts.
"We got him here on Saturday. He's trained well and I've got a decision to make. I've been following him for a long, long time.
"He's got all the attributes, but can he do it in the Premier League? That's the million dollar question."
