"It's highly flattering and I'm honoured to be linked with it," Bruce, who led Hull back into the Premier League after one season in the Championship (second-tier), told the local media.
"Whether or not it goes any further than that... It's the pinnacle isn't it? To manage your country, there's no bigger job.
"It's all speculation. There's a lot of people who have written nice things and I'm grateful for that."
The names of United States manager Juergen Klinsmann and Sunderland boss Sam Allardyce are also doing the rounds for the job.
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Bruce said he had not been contacted by the English Football Association and was focussed on building a Hull squad capable of competing in the Premier League in the coming season.
"With the players that we let go at the end of last season, and the two injuries we've subsequently picked up, we might now be looking at five or six new faces," he added.
"We'd like to add to the squad quickly if we could, but when you have European Championships going on there hasn't been any really significant movement (in the transfer market) just yet. A lot of clubs are being patient and we have to do the same.
"We have a good base of players here."
(Reporting by Simon Jennings in Bengaluru; Editing by Amlan Chakraborty)
