Following Brendan Rodgers' exit, former boss Martin O'Neill has been placed in interim charge while the side desperately search for a replacement in the hopes of reigniting their title chances against league leaders Hearts.
McKenna has been top of the betting odds, along with former Tottnenham and Nottingham Forest boss Ange Postecoglou. Now, McKenna was asked about the role in Thursday’s press conference, to which he said he cannot ignore such links.
"We've got a lot of Scottish representatives here today! It's not something 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 percent on the group here. 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 conversations. 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 sill in the middle of that.”
Celtic had been keen to explore a potential return for Postecoglou but McKenna is said to be second favourite if a deal is not reached. McKenna guided Ipswich to back-to-back promotions form League One to the Premier League between 2022 and 2024 and spoke more on the job which he admits entices him despite his focus being on Ipswich.
"I approach this job like I'll be Ipswich manager forever. I know that's not always going to be the case, but I'll always do my best as long as I am here...
"(Celtic) is a really big football club. Growing up, we all have our affinities. I don't think everyone has to go around and announce the club they support, but of course it's a really big football club, but we are in a really busy stage of our own season."
Celtic would have to pay McKenna'as £5M release clause if they did intend to snap him up, a cost many believe is not worth it considering Postecoglou is free.