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As far as we can tell, young Nathan Allan de Souza has been in London for about a week now, most likely undergoing a Chelsea medical, getting a tour of the facilities, eating some hotel food, and hanging out with fellow Brazilians like Philippe Coutinho.
The one thing that remains is signing the actual contract, which it would appear still has not happened. I'm no expert, but I think this is a fairly crucial step in completing the transfer. Until then, Nathan's biding his time in a hotel alongside his father.
Jose Mourinho commented on the Nathan situation a couple days ago as well.
"He's a player that our structure followed, and our structure thinks it's a player with potential for the future."
"If the deal is close, I will try to help him, as I try to help everyone, to become a Chelsea player. But he's not a player in my squad now, or a player I'm waiting for. I'm focused just on my job and my team."
-Jose Mourinho; source: Mail
Deals with third-party owners involved tend to be tricky propositions -- Nathan's only 70% owned by Atlético-PR -- so perhaps therein lies the crux of the delay. Either way, eventually he'll probably sign and then we'll get an official announcement.
NB. The Twitter profile @nathanallan10 is apparently fake. It would seem that the player's only social media account is on Instagram.