O'Neil took the Portman Road hotseat last month after McKenna decided to walk away, secure as a Town legend, following three promotions in four seasons.
That spell did include one relegation though, with the Blues tumbling through the top tier trapdoor in meek fashion back in 2024/25, their only top flight campaign under McKenna.
Indeed, Town's last good season in the Premier League was all the way back in 2000/01, when George Burley's newly-promoted side shocked the world by finishing fifth.
Kieran McKenna led Town to the Premier League - but couldn't keep them there (Image: PA)
Of his predecessor, O'Neil told Sky Sports: “Me and Kieran have exchanged messages a few times over the last few years, to be honest.
“I've spoken to him a few times at a few events. I've always spoken to him after games. He's obviously done an incredible job here.
“The next phase of that, which the club haven't been able to do for a very long time, is to secure a successful Premier League campaign.
“I think the last one was 2001, so a long, long time ago since the club have been able to really make a mark in the top level. That's what we're going to do this year. That's what everyone's focused on.”
O'Neil's got form in terms of keeping sides in the Premier League, having done it at both Bournemouth and Wolves - and he intends to make it a hat-trick in Suffolk.
Gary O'Neil has twice kept sides in the top tier (Image: PA)
“The aim is we need to stay in the division," he insisted. "Two seasons ago, the club didn't get anywhere near staying in the division. This time, we need to do better than that.
“That's why I'm here. That's why we're trying to get this squad ready. That's why we're trying to add quality to the squad from different parts of the world.
“We're trying to add some different attributes. We have to be successful this year. The club have worked hard to get its second go at a Premier League campaign.
“I think the beauty of this club is the following it has. You know that Portman Road is going to be full every week, no matter what.”
O'Neil joined Town after a short spell at French side Strasbourg. He led them to the semi-finals of the Europa Conference League last season – the first time the club had ever reached the last four of a European competition – and oversaw an eighth-place finish in Ligue 1.
Of deciding to head to Suffolk, he said: “I wasn't planning to be back in the Premier League this summer.
"I enjoyed my time at Strasbourg. It was excellent. I was managing in the semi-final of the European competition, the semi-final of the French Cup, (playing) PSG, Marseille.
“Big, big games to add to what I've already been doing over the last few years. And of course, the Premier League, as an English coach, is the place to be.”