The Spain international has been starved for game time under Los Blancos' new boss Santiago Solari – after being limited to just 78 minutes in his first five games in charge.
The Gunners are joint favourites to sign Isco in January at 10/1 along with Serie A champions Juventus.
The 26-year-old was dropped from the squad entirely for their Champions League clash against Roma and Solari said it was not due to injury.
The attacking midfielder was a key player under the former Madrid boss Julen Lopetegui, scoring twice in 14 games.
And with Isco's Madrid future in doubt, the bookies have also linked with him moves to AC Milan, Napoli and Man City.
Betfair: Isco's next club on February 3rd
Betfair Spokesperson Katie Baylis said: “With Isco seemingly out of favour with Solari at Real Madrid there is plenty of talk about him being snapped up by a number of clubs.
"Arsenal and Juventus are both at 10/1 to secure his services in the January transfer window, while AC Milan and Napoli are both at 14/1.
"While he could last out the season at Madrid, those odds could shorten considerably for the summer transfer if he continues to be overlooked at Real.”
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