The Red Devils came close to sealing a loan deal for the Portuguese ace over the summer, but saw their potential swoop for the defender thwarted by the passing of the transfer deadline.
Coentrao has only featured twice for the La Liga giants since then, and has been told that he is free to find a new club this month.
His agent, Jorge Mendes, is reported to have contacted United to assess their interest, which has opened the door for a move.
David Moyes is known to be keen to snap up a new left-back, with Patrice Evra set to leave the club at the end of the season once his contract expires.
Leighton Baines is rumoured to be their top target, but with the Toffees reluctant to sell their star man it appears that an agreement may be difficult to reach this month.
Coentrao, 25, is seen as a viable alternative, with his ability to play in a more advanced position also attractive.
The player himself is also said to be eager to make the move, with regular action ahead of the World Cup a priority.