Carrying reports from Spain, the paper claims Coentrao will be one of a number of players permitted to find a new club this summer by Bernabeu manager Carlo Ancelotti.
Manchester United were linked with Coentrao in the last two transfer windows, reportedly coming within hours on sealing a loan deal on deadline day last summer.
But the Portugal international stayed at Real Madrid although Marcelo continues to be Ancelotti's first-choice full-back when fit.
So far this season, Coentrao has made just six La Liga appearances with Real Madrid sitting top of the league.
He will be allowed to look for a new club, while the report also claims midfielder Casemiro and forward Alvaro Morata will also be allowed to move on at the end of the season.
Ancelotti already has a list of targets in mind, with Sevilla's Alberto Moreno reportedly his first-choice at full-back.
The Real Madrid boss is also eyeing up summer moves for Mario Mandzukic, Dortmund's midfielder Ilkay Gundogan, Juvenutus starlet Paul Pogba and Valencia midfielder Juan Bernat.
United may be in the market for a left-back this summer, with current first-choice Patrice Evra out of contract at the end of the season.
The Old Trafford defender has been heavily linked with a move back to France.