The Portugal international has emerged as a Gunners target in recent times, with scouts from the club having been monitoring his progress.
Coentrao has long been seen as one of Europe’s top attacking left-backs, but he has struggled for game time ever since joining Real from Benfica.
This has led to speculation that he could be available, and now Arsenal are plotting a bid, which is set to be accepted by the continental champions.
Real are keen to offload the £25m-rated star, which should smooth the process.
United have also been linked with Coentrao, and almost snapped him up during David Moyes’ reign, but were unable to beat the transfer deadline to land him.