With Antonio Conte having ruled himself out of the running and Spanish caretaker managers only allowed to take the helm for a period of 15 days, Wenger's considerable experience and availability had seen him proposed as a potential successor to Julen Lopetegui at the Bernabeu.
Santiago Solari has overseen three wins from three during his time in interim charge, but Madrid must come to a long-term decision following their game against Real Valldolid at the weekend as Solari's 15-day grace period comes to an end.
However, it seems that Wenger will not be the man chosen to fill the hot seat in the Spanish capital, with the man himself insisting that he has not been contacted by the reigning European Champions.
"I haven't made any decision on my future yet," Wenger told 'beIN Sport'.
"Do I go straight away into management again or not? To be honest Real Madrid have not come back to me so I have not had to turn them down.
"I take every problem when I have to face it and try to find a solution. At the moment I do not have that problem. I will decide in January what I will do."
The veteran manager has been out of work since leaving Arsenal at the end of last season and has also been recently linked with the AC Milan job as Gennaro Gattuso continues to struggle, though the 69-year-old later labeled those reports as "fake news".