The 31-year-old made his debut in Nigeria's 3-1 friendly win against Venezuela last month.
Ameobi, who was born in Zaria, northern Nigeria, before moving to England with his parents at the age of five, has just returned from a groin injury.
Shola Ameobi: "Every professional player loves to play at major tournaments and I'm no different.
"I need to earn it because the are several players out there equally deserving of that chance to represent a country like Nigeria
"You can call me a late bloomer at international level but I'm grateful to God for this big opportunity.
"The African Cup of Nations is what the European Championship is to others - so it will be a dream come true to represent my motherland.
"This is a big chance and I know this is the closest for me. Hopefully, I can live that dream when and if selected.
"I need to earn it because the are several players out there equally deserving of that chance to represent a country like Nigeria.
"There's always that healthy rivalry to fight for a place.
"You just need to keep giving your best and hope to stay fit and healthy.
"The club is still in Europe and Nigeria is preparing for a big tournament. It's a big honour to be considered by both."
Nigeria will take on Zambia, Ethiopia and Burkina Faso, in Group C of the tournament, which takes place between 19 January and 10 February.