The La Liga giants had want to recoup the €30m they paid for Coentrao from Benfica in 2011, but the Sport report claims Carlo Ancelotti's side have dropped his asking price to €25m.
Coentrao is reportedly keen to leave Madrid in search of first-team football, something that may be on offer at Old Trafford next season.
David Moyes is expected to lose Patrice Evra at the end of the campaign, the Frenchman is out of contract this summer.
The defending Premier League champions reportedly came close to landing the Portugal international on loan during the summer transfer window.
And they were linked again with Coentrao during the January window, although no deal was agreed between the two clubs.
However, United executive Ed Woodward has confirmed Moyes will have money to spend this summer - which opens the door to a renewal of interest in Coentrao.
If Evra leaves, United will need to bring in another full-back. Current back-up Alexander Buttner has failed to impress in his limited outings in the first-team this season.