Nathan Allan de Souza goes back to Brazil on Wednesday [yesterday]. The attacker must complete in his homeland paperwork to get the work permit in order. Once the formalities have been completed, Nathan returns to the Netherlands as soon as possible to conclude definitely on the A-selection.
Since January 2012, Brazilian citizens are allowed visa-free entry and travel around the European Union (and vice versa), provided their stay doesn't exceed "90 days within a 180 day" period.
Nathan's case, though, is obviously different. He is expected to spend at least a year in the Netherlands, and he's going to be working and getting paid. While he could travel freely to meet and sign with Chelsea and then with Vitesse, he now needs to obtain a work visa. There is no universal work permit in the EU; each country calls its own shots in that regard. And apparently to secure a Dutch work permit, Nathan has to first travel back to Brazil.
"He must surrender his passport at the Dutch embassy in Rio de Janeiro. That goes for a passport stamp to Washington [DC?]. Nathan must then wait in Brazil, he is [not] allowed without a passport [to] leave the country. It may take up to ten days before the passport back."
-Peter Bosz; source: Vitesse
So, provided there are no unforeseen obstacles or objections, it should all be sorted out very soon, and ideally before Vitesse face their first competitive matches of the season at the end of the month in the Europa League third qualifying round. Hopefully this won't disrupt Nathan's preparations for the new season too much.