Ipswich's manager and Wales head coach have been connected with the Scottish champions manager position
The Championship club's their manager says he has had "zero conversations" with the Glasgow club about their coaching position, while Wales national team manager Craig Bellamy is dedicated to completing his squad's international campaign.
Both have been linked with the manager's job at the Scottish champions following the former manager's resignation on Monday.
McKenna referred to the Glasgow giants as "a really big football club" but stressed he is "in the middle" of a "extensive rebuilding" with the Championship side.
The 39-year-old assumed control of Portman Road in recent years and led them to the English top flight with back-to-back promotions, but they managed only four games last season as they were demoted back to the second division and they presently occupy 12th in the Championship.
"There have been any of those discussions," the English capital native ex- Northern Ireland youth international said when questioned about being on the candidate list.
"It's not something I have given any thought to, or where any part of my concentration is currently.
"I have a special position here at a special team. And we're at a crucial stage of the campaign. Everything external hasn't reached my awareness."
It has been suggested that McKenna would be willing to talk to the Scottish side given his boyhood allegiances.
"During youth, we all have our affinities," he said when questioned about these. "It's unlikely all people has to go around and announce what they used to be, but of course it's a massive sports organization."
The coach signed a new four-year contract in 2024 and was questioned about his reported £5m release 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 anyway!
"I tackle this job like I'll be Town's coach indefinitely. I understand that's not always going to be the situation, but I will consistently give maximum effort as while I remain in position."
The former striker represented Celtic on temporary transfer from Newcastle United in the mid-2000s, but the former Wales striker is inclined to finish the current global tournament qualification, a stance that would practically eliminate the mid-forties from immediately taking the Celtic job.
The Welsh squad are currently in third place in their qualifying group behind group toppers the Red Devils and runners-up North Macedonia.
Wins over the minnows and North Macedonia in next month would book their place in the qualification play-offs, but they are all but guaranteed of reaching that stage, thanks to a productive Nations League performance, even if they not end up their group runners-up.
Considering his present position, Bellamy, whose agreement expires after Euro 2028, would not be available until following the play-offs at the earliest.
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