The 42-year-old former Republic skipper is due to give his first press conference since being named as O'Neill's assistant on Wednesday with the media eagerly anticipating his appearance.
However, while the manager is adamant that it is he who is in charge, he has no intention of telling Keane what he can and cannot say.
O'Neill said: "I am going to try to clear something up here: I am not Roy's father, absolutely not.
"He can look after himself, he can say what he wants. Seriously, he is under absolutely no gagging at all and I am quite sure I would not even have to have that conversation with him.
"I am not going to sit there saying, 'Don't say this, don't say that'."
The pair met the players for the first time on Monday evening and conducted their opening training session the following morning.
O'Neill admits both parties are still getting to know each other, but he is determined to treat his squad as adults as he sets about the process of stamping his own mark on the team.
Asked about discipline, an issue which often taxed predecessor Giovanni Trapattoni, the 61-year-old said: "Well, you must remember I grew up, I played under one of the most mercurial managers there ever was in Brian Clough.
"Brian Clough would have come down on an evening the night before a game when we were staying, let's say, in London and said, 'Lads, do you want a glass of wine with your meal?'.
"That would have been unheard of. He was so unorthodox, he was off the wall, but he had a philosophy that he was dealing with men and that if they couldn't look after themselves...
"He did not expect if he left the room that these boys would have five glasses of wine. He gave you some leeway. You go across that leeway and he would have cut you in two.
"I don't know, but just hearing the stories, I think Jack [Charlton, former Republic manager] was kind of like that, treating the boys like men. In other words, if you win the game, I will give you some free time.
"I'm kind of like that, and I think John O'Shea would tell you. Winning the games is very, very important. If you've won and you've worked for it, you should be allowed a little bit of time to let your hair down, if that's the case."
Meanwhile, O'Neill confirmed that the Football Association of Ireland is investigating the possibility that England Under-21 striker Connor Wickham could be eligible for the Republic.
He said: "If someone tells me someone is available, particularly someone I have worked with and might have a chance, I would give it some consideration."