The Ivory Coast man has not played for United since returning from international duty, and has now missed the last eight games.
And it appears a return is not on the horizon, with Mourinho saying the injury is not healing as expected.
"I think it's serious," he said after the win against Bournemouth. "We are trying a conservative treatment but if the conservative treatment is not working, he might have a surgery procedure. Probably the doctor can inform, it is not a problem for me, we don't want to speak about it."
"I don't want to be pessimistic, I want to leave it with the doctor."
The good news for United and Mourinho is that central defence is the one position where the club has very good depth.
"But today, we play with [Chris] Smalling and [Phil] Jones, [Victor] Lindelof on the bench, Marcos Rojo is injured but nothing really big so during all season we have problems with central defenders. Chris Smalling is playing amazingly well, so we are fine," he added.