Hertha are prepared to sell the 16 year-old for €20m this January market.
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Despite his youth, Eichhorn is playing regularly for 2.Bundesliga Hertha's first team this season.
Real Madrid, PSG and Barcelona are also watching the defensive midfielder, says BILD.
"He is an incredible, exceptional talent," Hertha teammate Fabian Reese hailed following the 16-year-old's debut. "If he continues like this, all doors will be open to him.
"I have rarely seen anyone so talented at that age. He has a huge career ahead of him."