Germany centre-half Koch will be sidelined for around three months following a successful knee operation, while Spain international Llorente could be out for up to three weeks, Bielsa said.
Koch, who had surgery on Tuesday, had been playing with a knee injury since arriving from Freiburg in the summer and damaged it further in last week’s defeat at Chelsea.
Bielsa said: “The surgery went well and the length of Koch’s absence depends on the evolution, but he’s likely to be out for around three months.
“It’s a shame to miss him for such a period of time, but during a season this is normal for injuries like this to happen to a team.”
Bielsa said Luke Ayling, Pascal Struijk, Kalvin Phillips and Gaetano Berardi, who is working his way back from a long-term knee injury, would provide sufficient cover in central defence.
“We’re not thinking of the possibility of bringing another centre-back into the team,” Bielsa added. “And apart from that we also expect to count on Berardi from February.”
Midfielders Pablo Hernandez (muscle strain) and Jamie Shackleton (thigh) have recovered from their respective injuries and will be available to face West Ham.