According to French newspaper L'Equipe, the Chelsea striker told team-mates that he was to withdraw from Cameroon duties following their 1-0 FIFA World Cup qualifying win over Libya on Sunday.
However, Finke avoided commenting directly on the issue, saying that he is keen for Eto'o to clear up his own future.
"Samuel Eto'o is a great player and it is better that he should be the one to explain things, he is the one who knows his decision," he said.
"He has given a lot to football and Cameroon and that is why he is the one to explain this."
The win over Libya ensured that Cameroon will feature in the third round of qualification.
Finke took over the role of manager after Jean Paul Akono was forced to step down due to illness and the German paid tribute to his predecessor after the win.
"I present my greetings to Jean Paul Akono, who was responsible for the first three matches and the victory today," he continued.
"This is something Jean Paul Akono participated in and he did a good job, I hope his health will get better."
Cameroon are now just one two-legged tie away from the World Cup next year, having been eliminated at the group stage in South Africa in 2010.
