The new Republic of Ireland assistant manager was described as an "intimidating, ferocious individual" in the former Manchester United boss' autobiography released in October
Sir Alex described his former captain as an "intimidating, ferocious individual", adding that "he has the most savage tongue you can imagine".
Keane responded soon after, questioning the Scot's need to criticise former players and now, in his first press conference in his new role with Ireland, revealed he would address the issues surrounding the pair's strained relationship.
"The beauty of football is everyone has opinions and I've no problem with that," he said when questioned on Sir Alex's book.
"The issue I'll have with, with anybody who seems to talk about me or has issues with what I've said in the past and people tell lies about me, that's when I'll come out and defend myself.
"Well I'm not going to sit here and defend myself regarding Alex Ferguson. That's for another day."
Meanwhile, with Ireland set to face Latvia on Friday under the control of Martin O'Neill for the first time, Keane has said the offer to work with the former Sunderland and Aston Villa manager was "too good to turn down".
"I’ve seen some of the matches and there’s the emotional attraction to it,” said Keane of his return to the Ireland set-up.
“I always think Ireland should be getting better results. It was the same when I was a player. I suppose that was one of the reasons I used to get frustrated. I used to think that we should be doing better than what we were doing.”
"I’ve got massive respect for Martin. We’re certainly not buddies but hopefully we’ll work well together."
Keane concluded his press conference by proclaiming that his heart is fully invested in his new post and that too much has been made of his temper in the past.
"I’m not some sort of animal. I’m a footballing man. I like to work hard and push people,” said Keane. “Sometimes I suppose I have got that slightly wrong on one or two occasions over the years, but generally speaking I look back and I think I got a lot of it right."