Mancini wants to take charge of an African team for the tournament and also next year's World Cup.
"I renounced a lot of money, but if I were to have stayed on the payroll until the final day of my contract I would have gone under everyone's radar. I would have the money, but not the happiness that comes from coaching," Mancini said.
"I love coaching, and I consider it to be as one with playing football.
"I was asked in an unofficial way whether I am available. I said that I am because the prospect of coaching a team in the African Cup of Nations and the World Cup fascinates me, and Nigeria is a country that is rich with great players who aren't celebrated enough.
"If they really want me, I will sit down and talk."
After revealing his interest in taking over a national team, Mancini also announced his interest in replacing Marcello Lippi as the trainer of Italy after the World Cup.
He added: "The answer is yes if you somehow think that by accepting a job from Nigeria I would refuse Italy But it's not a self-candidature. Do not present it as such. You asked me a question and I have given you a response."