The midfielder has started seven of Arsenal's last eight games and is due to finish the season at the Emirates before returning to Real at the end the season.
But Arteta hopes the Spain international remains part of his side next season.
"We are talking to the club," said Arteta
"Obviously we don't own the player, he's not in our hands, so the clubs will need to have a communication and see what we can do."
Arteta added: I'm really happy with him. The way he's evolving and I love how much he likes to play football – the passion he puts into every training session, and in every game, you just have to see his celebrations.
"Whether he's on the pitch or on the bench, the way he celebrates [shows] how much he puts into it. Again, I'm really happy with him, I think he's evolving in the right way and he's becoming a really important player for us."