The Belgium winger comes off contract at the end of season.
Januzaj said: "I would always like to continue at Real.
"We will see, now I am here but many things can happen until January. I feel good at Real. Everyone knows that I have always felt at home and we will see how the future happens.
"For me the most important thing is to be well on the pitch and if things go well on the pitch, then more things can change."
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