The Indomitable Lions were crowned champions of Africa on Sunday, after they defeated Egypt 2-1 in the final of this year's Africa Cup of Nations in Gabon.
Nigeria will host Cameroon in a 2018 World Cup qualifier at the end of August, before they travel for the return leg four days later.
Amuneke, who was working as a pundit for Bein Television for the AFCON in Gabon, said: “Yes, Cameroon are a good team. Tactically they improved with every game with different approaches during the AFCON.
“They deserved to be champions. They were very determined and how they approached every game was commendable.
“We therefore need to prepare very well if the super Eagle really want to beat this team in Nigeria because the confidence of the Indomitable Lions has grown after they were crowned African champions.”
The Eagles are top of their 2018 World Cup qualifying group with six points from two matches, while Cameroon are on two points.
Zambia and Algeria are on a point each.