Jose facing left-back headache for Valladolid
The Portuguese international had to be replaced midway through the first half of Real's Champions League match at home to Ajax Amsterdam on Tuesday after pulling up with what appeared to be a hamstring problem.
Standing in for Mourinho on Friday at a news conference previewing the Valladolid game, assistant coach Aitor Karanka confirmed Coentrao was unavailable.
"We are looking at different alternatives," he added, without giving any details about the seriousness of the injury.
Mourinho may opt to switch Alvaro Arbeloa across from right-back, with Sergio Ramos moving from central defence into Arbeloa's position and Raphael Varane slotting into the middle alongside Pepe.
Real's other recognised left-back Marcelo is recovering from a fractured bone in his foot and is not expected to return until mid January.
With unbeaten leaders Barcelona and second-placed Atletico Madrid not playing until Sunday, Real have a chance to trim the gap to the top two at Valladolid, who are seventh on 21 points.
Mourinho's side, who beat Atletico 2-0 at the Bernabeu last weekend, are third on 29 points, five behind Atletico, who host Deportivo La Coruna, and 11 behind Barca, who play at fourth-placed Real Betis.
Karanka, a former Real player, was also quizzed about persistent media reports that Mourinho will leave Real at the end of the season after his third campaign in charge.
"The coach is a strong person and he can't always be thinking and acting depending on the rumours coming out every day," Karanka said.
"The coach is focused on his day-to-day work here and preparing what we have and you have to forget everything else."