The 25-year-old full-back cost Los Blancos £26.4million when he arrived at the Santiago Bernabeu from Benfica in 2011, but has fallen out of favour under Jose Mourinho, starting less than half of the club's Primera Division matches in 2012/13.
His plummet down the Real Madrid pecking order has prompted rumours of a move to the Premier League at the end of the season, with both Chelsea and Liverpool credited with an interest in the Portuguese international's signature.
Reds boss Brendan Rodgers has already made clear his intention to add three or four quality signings to his Anfield squad when the transfer window reopens, while Stamford Bridge owner Roman Abramovich always seems to be willing to fund the acquisition of new players to improve an ageing Blues squad.
Chelsea were actually linked with Coentrao before he signed for Real Madrid, and could make a renewed effort to lure him to west London.
However, both Chelsea and Liverpool's hopes of landing the player have been dealt a blow after Tuttosport's claim that the left sided winger will form part of the deal to see Real Madrid sign £54million-rated forward, Cavani.
The Uruguayan is one of the most highly-rated striker's in world football at the moment, having scored 95 goals in all competitions since joining Napoli from Palermo in 2010.
Despite his fine form, the Spanish giants are unwilling to meet the Serie 'A' outfit's asking price for Cavani, but will offer £35million as well as Coentrao to sweeten the deal.