The 18-year-old currently plays in the Portuguese second division for Louletano, where he has been earning rave reviews.
Reis has been dubbed the new Luis Figo, and there has also been comparison with Nani and Cristiano Ronaldo.
Chelsea will need to fight off Inter Milan and Benfica for his signature.
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Meanwhile, Bayern Munich are reportedly interested in Everton full-back Leighton Baines.
The German side sent scouts to watch Baines at the weekend and are considering a £10 million bid in the summer