Kalou and his international team-mates were given a hero's welcome in Abdijan following their victory on penalties over Ghana in the final on Sunday, securing their second continental trophy.
However, the 29-year-old has yet to return to the German capital as previously agreed with the Ivory Coast ahead of the tournament.
"There was a clear agreement we received in writing from the Ivory Coast prior to the tournament, but apparently that got forgotten in the thrill of victory," said a frustrated Hertha general manager Michael Preetz.
"This is obviously not ideal, but Solomon is not to blame. He wanted to get away but could not.
"Fortunately, we only play on Sunday."
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