Los Blancos are monitoring the former Arsenal boss' situation, while a move into international football is the most likely move according to Betfair.
Wenger is believed to be ready to return to management in January.
The Japan national team are currently favourites to be Wenger's next destination at 5/1.
Meanwhile the 68-year-old's odds of going to Real Madrid have tumbled after their shocking start to the season.
Los Blancos have struggled for form under Julen Lopetegui and are winless in their last four games.
Meanwhile moves outside of Europe could see him join any Chinese club at 12/1 or any MLS sides at 14/1.
Betfair: Arsene Wenger's next move
Betfair Spokesperson Katie Baylis: “With reports that Wenger is planning a comeback at the start of next year, speculation is rife on where he is going and it’s largely being fuelled by Wenger himself.
"At this stage we have the Japan national team as favourites at 5/1 with Real Madrid next at 9/1 and any Chinese club at 12/1.
"There’s no doubt the announcement of Wenger’s next club will be absolutely massive around the world considering he was at Arsenal for 20 years, so we expect plenty of interest in this market.”
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