The Norwich boss has been linked with the Irish job vacated by Giovanni Trapattoni following the Republic's 1-0 World Cup qualifying defeat by Austria.
Hughton, who was born in England but qualified to play for the Republic through his mother, played 53 times as full-back for Ireland between 1979 and 1991. He also served as the national team's assistant manager under Brian Kerr from February 2003 to October 2005.
Hughton, however, steered Norwich to Premier League survival last season and brought in eight players over the summer, including Dutch striker Ricky van Wolfswinkel, at a cost of around £25million.
Hughton, who has been linked with the Irish job along with others such as Martin O'Neill and Roy Keane, said: "I understand my name has been mentioned along with other previous players for Ireland. It is absolutely just speculation.
"I am manager of Norwich, I am extremely happy here. We spent and invested more this summer than we ever have done. I have had support from the board here. I have a group of supporters who are fanatical and want this team to do well and I have the same challenges here as the supporters and the players have. I am incredibly happy here.
"There has been no official approach. We are a club I would like to think which is going in the right direction."
Hughton was coy on the question of whether he would like to manage the Republic some time in the future, not wanting to fuel any conjecture before Norwich face his former club Tottenham at White Hart Lane on Saturday.
"I can only answer questions to the appropriate people which is why my decision is to talk about how happy I am here at Norwich," said Hughton.
"Anything I might say over and above that might be construed in a different way. I was very proud to play for Ireland and I always want to see Ireland winning football matches but my responsibility is here.
"The club have shown great faith in me. They have spent very big in the summer. There is a project here, one started before I got here, and it is a challenge I am very much looking forward to.
"There will be some very good names mentioned. I don't know which way they will go but there won't be any shortage of candidates.
"For anybody who takes a job like that it is about timing. It is a different management philosophy (Premier League compared to international), a different week, the simple one is that it is day to day football and involvement with players (in the Premier League) and international level is not that. But it suits some people at some stage and others not."
Hughton said that he was not surprised by Trapattoni's sacking but added: "He's done a fantastic job there. We have to respect the fact that it is a nation that is not expected to qualify for all the championships that they enter. I am disappointed to see him go because he is a fellow manager."
Meanwhile, Norwich could see summer signing Gary Hooper make his first appearance in the squad this weekend after the former Celtic striker recovered from a shin problem.
"He has trained this week and he's fit," said Hughton.
"We will take a decision on when or if to use him, but he has come through with no problems."