The Elephants endured a disappointing World Cup, losing a dramatic game to Greece to crash out at the group stage, which prompted previous coach Sabri Lamouchi to resign from his position.
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"I'm going to become the new Ivory Coast coach; everything will be official in a couple of weeks," Trapattoni told Rai Radio 2.
"Morocco offered me a job too but I took 48 hours for myself and eventually chose Ivory Coast. Drogba? He's a great player."
Trapattoni also ruled himself out of assuming the presidency of the Italian Football Federation (FIGC), claiming that he was not prepared to merit such a high-profile role.
"I don't think [it] would be a good idea, it's a very important job and I didn't study enough to deserve it," he said.
Trapattoni, who has served as boss of AC Milan, Juventus, Inter and Bayern Munich in a stellar career, is one of only four coaches to win league titles in four different countries.