Some reports have suggested that the 55-year-old will be spoken to by Football Association technical director Dan Ashworth about the vacant England post this week.
But Bruce has stressed that he has not been approached by the FA.
He is currently in Portugal with Hull preparing for the club’s forthcoming campaign back in the Premier League and while he is treating links to the England post as pure speculation, he says he admits he is seriously flattered to be mentioned as a possible contender.
Bruce said: “It is highly flattering and I am honoured to be linked with it.
“Whether or not it goes any further than that... it is the pinnacle, isn’t it? To manage your country, there is no bigger job. (But) it is all speculation.
Adamant that Hodgson’s replacement should be English, Bruce added: “Not just because I am English, but I hope they do.
“All these lads do their coaching badges, A licences, pro licences. In my opinion the top of the FA should be English. I have always said that.
“There is no one more patriotic than I am and to be linked with it is testament to the fact we are in the Premier League and there is only four or five English managers.”
Sunderland manager Sam Allardyce and ex-Germany boss and current United States head coach Jurgen Klinsmann are the frontrunners to fill the breach left by Hodgson, who resigned following England’s ignominious last-16 exit from Euro 2016 at the hands of Iceland.
But Bruce himself is also not without his admirers, with the north-easterner’s claims for the England role having been endorsed by former striker Alan Shearer, who feels the Tigers’ chief is a perfect fit for the position.
Shearer said: “I get that there is not a huge list of suitable English candidates. But there are people out there who should be considered and spoken to.
“Why wouldn’t they give it to Steve Bruce? He would be my pick. Bruce has worked in English football all his life.
“He knows the game inside out and is widely respected. He has played at the highest level with Manchester United.”
Meanwhile, the Tigers have been handed a pre-season blow with experienced duo Allan McGregor and Alex Bruce set to be sidelined for up to six months.
Scottish international McGregor is to undergo back surgery, while Bruce will go under the knife for an Achilles operation on Thursday.
Bruce has admitted that he is interested in signing Wales’ Euro 2016 star Hal Robson-Kanu, with the Tigers also in discussions to sign Senegalese international defender Lamine Sane, 29, who plays for Ligue One side Bordeaux.
On free agent Robson-Kanu, 27, whose goal against Belgium in the quarter-finals was voted as the goal of the tournament, Bruce said: “We are booked in for talks with him and to see him in the next few days.
“Do we intend to offer him a deal? Yes.”