The Spanish midfielder is out of favour at Real under manager Carlo Ancelotti.
And the Italian boss revealed some of Real's plans for the January transfer window in a recent interview.
"I don't like January signings much," Ancelotti told reporters.
"If we have players who aren't happy, it's something we can think about but we are not going to sign anyone.
"We have enough to compete until the end of the season."
Such news is likely to be a boost to the Gunners, who have been linked with Isco in the British and Spanish press in recent months.
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