The talented teenager has impressed in the academy, scoring seven times against Norwich's Under-18 team last weekend.
He also netted a whopping ten goals against Liverpool's youth side earlier this season.
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The Telegraph claim that due to being dual nationality, he could be offered a deal by teams around Europe before Arsenal can commit him to a professional deal.
The likes of Bayern Munich are said to be in for the English-Danish youngster.
Obi-Martin has played for both England and Denmark's youth international teams.