The Tractor Boys boss penned a new deal through to the summer of 2028 in May following back-to-back promotions.
It came amid reported interest in McKenna from the likes of Brighton, Chelsea and Manchester United.
Chairman and CEO Mark Ashton has now lifted the lid on how in demand his manager was during the summer.
Asked if United had come in for McKenna, Ashton told White & Jordan: "Top clubs came in for him this summer, I'm not gonna say who."
Jim White pressed him on United, prompting a smile before he added: "I'm not going to say who because I'll get myself into trouble but top clubs came and knocked the door. It was real."
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Ashton was also asked about Brighton as he continued: "You're good Jim, my job was to sit down with him and show him the virtues of Ipswich, talk to the other clubs that had knocked the door and said this is why I believe we are right for you."
McKenna was appointed by Ipswich in December 2021, his first senior managerial role.
He left United to take the role, having been an assistant under Jose Mourinho, Ole Gunnar Solskjaer, Michael Carrick and Ralf Rangnick.
The Northern Irishman had also been under-18s manager and a scout at Old Trafford.
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Since arriving at Portman Road, though, he has won promotion in each of his full seasons to go from League One to the Premier League.
McKenna has also won 77 of his 143 matches at the helm, most recently against Tottenham before the international break.
That win was Ipswich's first since returning to the top flight.
It came after a 10-match winless run to start the season, but Ashton remained intent on sticking to their beliefs, explaining: "We've stuck to the plan.
"We recruited Premier League staff and good players into League One that we believed with the right head coach, the right infrastructure could take us right through to the Premier League.
"And again, we win away for our first time at Ipswich at Tottenham last week and we've got League One players on the pitch. So the journey has been fantastic."
The win at Spurs leaves McKenna's side 17th in the table ahead of the visit of United on Sunday.
Nicky Butt claims Ipswich boss Kieran McKenna is the BEST coach he's EVER seen and would be a success at a bigger club