It comes just a week after Bruce was fielding questions about his future with the Tigers after a 3-0 home loss to Newcastle saw them slip into the relegation zone.
The Tigers boss was also tipped to succeed Alan Pardew at Newcastle United earlier this season.
Bruce said he is focused on Tuesday???s crucial game with Aston Villa and the latest rumours are disrespectful to Cottagers boss Kit Symons.
He said: “I was getting the sack the day before, and then Fulham want me.
“The biggest problem I’ve got with the whole thing is they’ve got a manager in situ at Fulham and I’ve got huge respect for Kit who is new to the job.
“I can’t comment on it because if I comment on it it just fuels it even more, and as far as I’m concerned it’s rubbish journalism.”
Saturday’s 1-1 draw at Manchester City has provided a timely confidence boost to the Tigers and Bruce knows the next month could shape the club’s top-flight future.
They face QPR, Stoke and Sunderland in the next month and the Hull boss has demanded his players match their form against the big clubs in the crucial relegation scraps.
“This cluster of games we have coming up are going to be crucial to us,” added Bruce.
“We’ve got to show the resilience and attitude we had at Liverpool and Arsenal and Manchester City.
“That’s where we were very good last year – we beat the teams around us and unfortunately this season we haven’t done that, and we have to address it over the next few weeks.”
Bruce could recall new boy Dame N’Doye and fellow striker Nikica Jelavic to his starting line-up for the visit of Villa after both started on the bench against City.