Trapattoni's five-year reign as Republic of Ireland manager ended this week, following the 1-0 defeat to Austria on Tuesday.
Alongside Martin O'Neill and Mick McCarthy, Hughton features prominently in the betting markets for the vacant post, but he insists he is happy with life in Norfolk.
"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," he said.
"I understand my name has been mentioned along with other previous players for Ireland. It is absolutely just speculation.
"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.
"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."
Hughton won 53 caps for the Republic from 1979 to 1991 and played in all three matches at the Euro finals in 1988.
He also served as the national team's assistant under Brian Kerr, from February 2003 to October 2005.
Meanwhile, Hughton said summer signing Gary Hooper could make his first appearance 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."