The duo were confirmed as taking charge of Ireland earlier this month, with some raising their concerns about the effect of the outspoken nature of Manchester United's former captain.
However, while O'Neill has reiterated that he is the one calling the shots, he won't restrict Keane from expressing his views on certain issues.
"I am going to try to clear something up here: I am not Roy's father, absolutely not," O'Neill told the press.
"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'."
Ireland host Latvia in a friendly on Friday.