Brendan Rodgers handed in his resignation on Monday (October 27) following Celtic’s 3-1 Premiership defeat to leaders Hearts.
Celtic are now on the lookout for a manager to take them into a brave new era and have been heavily linked with a move for Ipswich boss McKenna, 39.
McKenna has since opened up about the links, saying: “It’s not something (the Celtic vacancy) I have given any thought to, or where any part of my concentration is.
“I have a special job here at a special football club. It’s a massive club. We’re at a really important stage of the season, starting on Saturday at QPR. My focus has been 100% on the group here.”
He continued: “My focus is honestly just on Ipswich. I know the size and significance of this football club. So there is no time or space to discuss any other football club.
“I have not had any of those (formal) conversations (with Celtic). My focus has been here.
“I’ll work here as if I am going to be here forever, and I have done since the day I came here. When I arrived, I always knew it was going to be a long-term project.
“We are still in the middle of that. (Celtic) is a really big football club. Growing up, we all have our affinities, but we are in a really busy stage of our own season.”
When asked about rumours of a £5 million release clause, McKenna smiled: “In every manager’s contract, there are always contractual things. I don’t know what they are, and if I did, I wouldn’t tell you anyway!”