The 15-year-old midfielder enjoyed a successful five-week trial with the Stamford Bridge club over the summer, impressing Chelsea coaches including first-team boss Jose Mourinho.
And Portuguese newspaper A Bola, citing reports from Italy, claims Chelsea will pay a compensation figure to Zawisza Bydgoszcz, the club where Adamczyk currently plays his football.
He would not be able to feature for the Blues until June 2014 at the earliest - once he's finished high school - but the report claims the deal will be agreed in principle in the January window.
The attacking midfielder was reportedly first spotted by Chelsea's Poland scout Janusz Oledzki.
He would be the latest talented teenager to move to Stamford Bridge following the deal that brought highly rated Burkina Faso international Bertrand Traore to the club in October.
The Blues have one of the best academies in the Premier League, with high hopes for past and present academy stars like Nathaniel Chalobah, Nathan Ake, Patrick Bamford, Ruben Loftus-Cheek, Wallace, Cristian Cuevas and George Saville.
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