“[It was] fairly innocuous for Max but a decent enough bang, we just hope it’s on the lesser side of it than too serious.
“But I think both of those are going to be a potentially decent enough rehab period.”
Llewellyn played in three of Wales’ four internationals last month with the Six Nations campaign set to begin in eight weeks.
The 26-year-old missed a couple of matches earlier in the campaign for Gloucester but Skivington said this was a new injury.
Versatile Joseph has played in all six of Gloucester’s Prem matches since signing this summer and started on the wing for their latest European match.
“[He] got his ankle caught between a couple of bodies. He’s non-weight bearing at the moment. The fact he’s on crutches probably isn’t a great sign,” Skivington added.
Gloucester are back in European action on Saturday with a trip to Munster before returning to the Prem on 19 December – away at Leicester – followed by a home fixture with Saracens on 27 December.
The Cherry and Whites do however have vice-captain Arthur Clark available for the first time this campaign, while Jack Clement also returns for the first time since the opening match of the season in a boost to their forward pack.
