The Boys in Green head coach has dismissed the notion that his assistant manager has been warned about speaking to the media
The duo took their first training session with the Ireland team in Malahide on Tuesday and Keane is expected to give a press conference on Wednesday ahead of Friday's friendly with Latvia at the Aviva Stadium.
And O'Neill, who requested to have the former Sunderland and Ipswich Town manager as his assistant, has stressed that the 42-year-old was not under "gagging" orders.
"I am going to try to clear something up here: I am not Roy's father, absolutely not," he told reporters in Dublin.
"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 Ireland boss also addressed the issue of discipline within the squad, suggesting that he would attempt to give players "leeway" where possible. Noting his experience as a player under Brian Clough at Nottingham Forest, the 61-year-old said that there must be a degree of trust between the management and the players.
"Well, you must remember I grew up, I played under one of the most mercurial managers there ever was in Brian Clough," he said.
"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."
The Republic of Ireland host Latvia on Friday November 15 before travelling to Poznan to face Poland four days later.