Just 16, Eicchorn has made 14 senior appearances for Hertha and drawn comparisons with Real Madrid great Toni Kroos.
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Real have been watching the youngster's progress over the past 18 months and were expected to make a move for him this summer.
However, journalist José Miguel Villarroya says while Real Madrid are keen, they're trailing Bundesliga interest in Eicchorn.
He told La Journal du Real: "He's a 16-year-old midfielder from Hertha Berlin. He plays in the German second division. In Germany, he's being talked about as the new Toni Kroos.
"However, as far as I understand, he's about to sign for Eintracht Frankfurt."