Rather than dismiss the idea out of hand, let me first ask what do you mean by a "great power"?
If you mean great in the same ways that France or the UK were great during the 20th century, then the chances are very poor. If, however, you mean something more like a regional power - like, say, India or Australia - then it might be more possible. I don't know much about Nigeria, but I seem to recall there's a lot of potential in terms of wealth and an educated population if it can just be brought to bear.