Hull boss Steve Bruce was interviewed by the Football Association on Monday about the England manager’s job.
Sunderland boss Sam Allardyce has also been interviewed and is favourite to succeed Roy Hodgson, who quit after England lost to Iceland at Euro 2016.
Hull said Bruce, 55, has “held informal discussions” but “no official approach has been received from the FA”.
“It’s got to be the prime job that any Englishman could ever want to have,” Bruce told Sky Sports.
“I’m highly flattered to be even considered. I put my case across and let’s hope it was successful.”
Bruce added he was up against “a big pal of mine” in Allardyce, and that whoever gets the job needs to take away the players’ “fear in tournaments” after a run of just one win in seven matches at the 2014 World Cup and Euro 2016.
Bournemouth manager Eddie Howe and USA coach Jurgen Klinsmann have also been linked with the role.
Bruce led the Tigers back into the Premier League last season after relegation to the Championship in 2015.
Hull’s statement added they want the FA to “conclude their business quickly in order to avoid further speculation”.
Sunderland called on the FA to “bring about a swift resolution to the matter” after Allardyce was interviewed last week.
FA chief executive Martin Glenn is fronting a three-man panel, which also includes FA technical director Dan Ashworth and board member David Gill, to decide the next England manager.
Former Manchester United captain and defender Bruce, who was never capped by England, said in June that he would be staying at Hull.
However, amid talk of a takeover at KC Stadium, he accepted he could be replaced when asked if he was certain of his position.
Prior to talks with the FA, Bruce recently said it was “highly flattering” to be linked with a role he hopes goes to an Englishman.
“There’s nobody more patriotic than I am,” he told BBC Radio Humberside.
“I’m honoured to be linked with it. It’s the pinnacle to go and manage your country. What bigger job in the world is there?”