“When you look at the Senegal team, they have Sadio Mane and deserved it [World Cup qualification], so with hard work I think they will do well," Atsu told Voice Online.
“The Nigeria team have a lot of young players - very talented players - who are playing at a high level.
"So I believe Nigeria will be one of the countries to go far in the World Cup."
Africa's best position at the World Cup since debuting in 1934 has been quarter-final berths achieved by Cameroon, Senegal and Ghana in 1990, 2002 and 2010 respectively.
“Also Egypt - they have Mohammed Salah, they have a very good coach [Hector Cuper] and they play really compact," Atsu added.
"I have played against them and they are really hard to play against.
"I believe they can also go far.”
Tunisia have England, Belgium and Panama to battle in Group G, while Senegal, who are set to return to the global showpiece for the first time since debuting in 2002, will square off against Poland, Colombia and Japan in Group H.