Ipswich's manager and Wales head coach have been connected with the Celtic manager position
The Championship club's their manager says he has had "no discussions" with Celtic about their coaching position, while Wales national team manager Craig Bellamy is committed to seeing out his squad's international campaign.
Both are being considered with the manager's job at the Scottish champions following the former manager's departure on the start of the week.
McKenna described the Glasgow giants as "an enormous soccer institution" but emphasized he is "deeply involved" of a "long-term project" with the Championship side.
The mid-thirties assumed control of Ipswich in recent years and led them to the Premier League with back-to-back promotions, but they managed only four games last season as they were relegated back to the Championship and they currently sit 12th in England's second tier.
"There have been such conversations," the London-born former Northern Ireland young player said when asked about being on Celtic's shortlist.
"It's not something I have considered seriously, or where any part of my concentration is currently.
"I have a unique position here at a special club. And we're at a crucial stage of the season. Everything external hasn't reached my radar."
Reports indicate that the manager would be open to speaking to Celtic given his childhood support.
"During youth, we all have our preferences," he said when questioned about those. "I don't think all people has to publicly and declare what they were, but naturally it's a really big sports organization."
McKenna agreed to a fresh four-year contract in 2024 and was asked about his reported buyout clause.
"In every manager's contract, there are things," he replied. "I don't know what my specific terms are and, were I informed, I wouldn't disclose you regardless!
"I tackle this role like I'll be Town's coach forever. I know that's not invariably going to be the situation, but I'll always do my best as long as I am here."
Bellamy played for the Hoops on temporary transfer from the Magpies in 2005, but the ex- Wales forward is minded to finish the current global tournament campaign, a stance that would practically eliminate the 46-year-old from immediately taking the Glasgow position.
The Welsh squad are presently in third place in their World Cup group behind group toppers the Red Devils and runners-up North Macedonia.
Wins over the minnows and North Macedonia in November would book their place in the final qualifying round, but they are virtually guaranteed of reaching that stage, due to a productive European competition campaign, even if they fail to end up their group second place.
Considering his current position, Bellamy, whose agreement expires after the European Championship, would not be available until following the qualifying matches at the minimum.
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