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Mourinho was not able to name the specific injury that Bailly is suffering from although he had trouble with his groin after returning from international duty with the Ivory Coast.
"I think it is serious. I don't know (how long he will be out). It is an injury that came from the last time he was with the national team," Mourinho said.
"We are trying a conservative treatment but if the treatment is not resulting then probably it will end in a surgery procedure but let's wait a little bit more," he added.
United, with Chris Smalling and Phil Jones in the centre of defence, beat Bournemouth 1-0 on Wednesday. Mourinho also has Marcos Rojo and Victor Lindelof as options in the back line.