The national side begin their campaign in South Africa tonight against Burkina Faso in the opening Group C clash.
"I have got good friends there, like Victor Moses and John Obi Mikel, and a lot of others as well," Anichebe told the club's official website.
"I want them to do well and it will be great for Nigeria if they can because last time they weren't in the competition. Hopefully they can go there and make Nigerians proud."
Anichebe hasn't competed for his country since 2011 when he suffered a groin injury.