Los Blancos want to fetch £10m for the 26-year-old, who was strongly linked with a move to Old Trafford last summer, according to the Daily Star. United boss David Moyes is in the market for a new left-back - Patrice Evra is still yet to sign a contract extension with the Red Devils - and the Scot might consider the Portuguese as a cheaper alternative to Southampton's Luke Shaw.
Shaw, like Coentrao, has been linked with a move to Chelsea over recent months. The 18-year-old England international, however, is expected to cost at least £30m, which could deter Moyes from making a bid this summer.
Chelsea, meanwhile, may not bid for either Coentrao or Shaw because of the fine form of Cesar Azpilicueta. Blues boss Jose Mourinho has been impressed by the Spaniard, who has displaced Ashley Cole in the starting line-up this season, and recently stated: "I think a team with 11 Azpilicuetas could probably win the [Champions League]".
Coentrao has made just six La Liga appearances for Real Madrid this season, with his current manager Carlo Ancelotti preferring Brazil international Marcelo at left-back. The Spanish giants have also been strongly linked with Sevilla full-back Alberto Moreno and AC Milan's Mattia De Sciglio in recent weeks.
A move for either will almost certainly spell the end of Coentrao's spell at the Bernabeu, while a move to the Premier League would look increasingly likely.