Endrick saw action for Real in their defeat to AC Milan last week.
The Brazil international told the club's website: "They're great players and I'm very happy to have the chance to play with them. Modrić set me up with an assist in training and I'm really happy. Madrid has amazing players and when we return to Madrid I'll be able to play with more of them. I'm going to ask them for advice because I'm here to work.
"It's a dream come true to be here, to train with my teammates, to score goals and help my team. I'm here in Chicago so I can help Real Madrid, that's what I'm here for.
"I've got a lot of fans in Brazil but I didn't expect all this here, all these fans. I'm very happy with all this. Madrid is the best club in the world and having all the love that the fans have for me is madness. If I could sign every fan's jersey I would."