Drogba has already withdrawn from their Africa Cup of Nations qualifier against Rwanda on Saturday and coach François Zahoui believes he may not return at all.
The 32-year-old had to have a hernia operation after playing at the World Cup this summer and is still working his way to full fitness, despite having scored four goals for Chelsea this season.
Zahoui flew to London to have talks with Drogba at the weekend and revealed: "He told me he was so tired that he wanted to withdraw from the national team for a while.
"Drogba is a world-class player who is indispensable for the Elephants but I had to respect his decision. We will let him recover his mental and physical strength and pray he comes back some day."