Sunderland’s Sam Alladyce remains the bookies’ favourite to succeed Roy Hodgson as the national team boss.
Both the current Black Cats manager Allardyce and ex-boss Bruce have held talks with the Football Association over the job.
And Bruce says there are other candidates in the running.
An FA panel of chief executive Martin Glenn, vice-chairman David Gill and technical director Dan Ashworth are believed to have also spoken to USA manager Jurgen Klinsmann, Bournemouth boss Eddie Howe and former England manager Glenn Hoddle.
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Bruce said: “I never quite made it as a player going back all those years ago and who wouldn’t (want the job)?
“If you’re English and it means something to you, who wouldn’t?
“It’s got to be the prime job that any Englishman could ever want to have. Yes of course it’s difficult, we know that, but there’s something in you.
“I am highly flattered to be even considered and extremely grateful to be considered. If anything happens, let’s see what the rest of the week brings and if it does, then happy days.”
Bruce knows he is up against some strong competition for the job, including his old friend Allardyce.
“You never know in an interview, I hope it went okay,” said Bruce.
“I put my case across and let’s hope it was successful. But then again I am up against a big pal of mine in Sam who has always done a good job over the years.
“And apparently there are some other candidates who are there too.
“To be in the mix, I am highly flattered because any Englishman for their salt would be extremely proud to be the England manager. What I said to them in the interview has to remain there, but we have to take away the fear especially in tournaments for sure.”