Furman spoke ahead of South Africa's quarter-final tie with Cape Verde on Saturday.
Recall that Nigeria's Super Eagles defeated Cameroon in the round of 16 to qualify for the last-8 where they will face Angola on Friday.
"I don't want to speak too soon because Cape Verde, we played them twice in 2017 in the World Cup qualifiers, we lost to them twice," Furman told the BBC World Service.
"2013 AFCON opening game at the FNB Stadium in Johannesburg, everyone expected us to win. It was a draw and if I'm honest, we should have lost that game so I'm not taking them lightly at all, it is going to be a very, very tough game but it is anyone's.
"The so-called big nations, the fancied nation Nigeria are going about their work in an understated fashion but I think they are ticking on really nicely so I would have them down as the favourites right now."
