The two Northern Irishmen will be in opposite dugouts when their two teams face off following the emotional week for Liverpool fans with the independent report into the Hillsborough disaster had been revealed to the public.
Rodgers is still looking for his first Premier League win as Liverpool boss, and O'Neill has proclaimed that the former Swansea coach will be able to manage the side on his terms.
"Brendan obviously has his style, which he brought to Swansea - I say brought to Swansea, it might have been there in the first place, but he certainly enhanced it," O'Neill told Sky Sports.
"If I say so, their start to the season under [Michael] Laudrup now is maybe a continuation of that work.
"People can tinker with it whatever way they want, but it's worked very well.
"On the back of that, he has gone to Liverpool and obviously wants to stamp his authority - or his mark, rather than authority, perhaps - on Liverpool Football Club. Obviously, that's what you want to do as a manager.
"But I don't think he's going into it with eyes closed. He would have had a number of meetings there with the owners of the football club. He must have agreed to the way in which they want to work.
"I believe there's a fly-on-the-wall documentary - I haven't seen it, so I really can't comment on it other than some of the reviews that people have made about it in the newspapers. It couldn't, maybe, have been done without his consent.
"But whatever way he is doing it, it's entirely up to him."