Wales boss Chris Coleman and former Everton man Roberto Martinez linked with Hull City job
Coleman guided Wales to the Euro 2016 semi-finals a month after signing a new two-year contract with the Football Association of Wales (FAW).
The 46-year-old has not been approached either formally or informally.
"We have had no contact whatsoever from the club regarding the speculation," said an FAW spokesman.
"All talks with Chris have been on how we can move forward after Euro 2016."
Bruce left Premier League new boys Hull after a breakdown in his relationship with vice-chairman Ehab Allam.
Roberto Martinez, sacked by Everton in May, and former Unites States coach Bob Bradley have also been linked with the vacancy.
Bruce, 55, joined the Tigers in 2012 and led them to promotion to the Premier League twice and also an FA Cup final appearance in 2014, losing to Arsenal.
FAW chief executive Jonathan Ford said earlier in July that he was hopeful Coleman would honour his two-year contract extension.
But Ford acknowledged it would be difficult to keep Coleman if he decided he wanted to manage a club side before then.
"At the end of the day we do have a contract that's been signed, but like anything, if somebody desperately says 'Well I'm not going to do the job', you're going to have a tough time keeping him," Ford said.
"There are procedures and there are policies in place with regards to if that does happen, but let's hope it doesn't."
The former Swansea City, Crystal Palace and Blackburn Rovers defender has also managed Coventry City, Real Sociedad in Spain and Greek side Larissa.
Wales begin their World Cup qualifying campaign against Moldova at Cardiff City Stadium on 5 September.
Coleman has been in charge of 38 internationals since his appointment in January 2012 and has overseen a remarkable transformation in Wales' - and his own - fortunes.
He made the worst start of any Wales manager, losing his first four games, but guided his country to their first appearance at a major tournament for 58 years with qualification for Euro 2016.
Coleman, who last managed in the Premier League with Fulham in 2007, has already said the 2018 World Cup campaign will be his last in charge of Wales.