The former Manchester United skipper was mauled by the Scot in his recently-published autobiography, prompting the 42-year-old to question his former manager's understanding of the concept of loyalty.
However, as he conducted his first press conference since being appointed as assistant to new Republic of Ireland boss Martin O'Neill, Keane was maintaining a diplomatic silence.
He said: "The beauty of football is everyone has opinions, I have no problem with that.
"The issue I will have with anybody who seems to talk about me or has issues with what I have said in the past, if people tell lies about me, that's when I will come out and defend myself.
"But I am not going to sit here and defend myself regarding Alex Ferguson. That's for another day.
"I am not really going to go into that too much. Football is about opinions, I have no problem with that, but when its lies, that's when you come out and say something.
"But today is not for that, today is just about talking, getting involved back with the Irish team, working with Martin, all positive.
"It's not an area I want to go into today."