Leeds have already lost the services of goalkeeper Jamal Balackman who has broken his leg and Bielsa revealed that Peacock-Farrell has also picked up a knee injury in training.
Centre-back Jansson, meanwhile, is also set to miss out with a foot injury picked up in the 4-1 loss at West Brom before the international break.
Jansson completed the full 90 minutes of the fixture but then flew back from international duty early to be assessed.
Asked about the fitness of Jansson, Bielsa said: "I think he won't be available for this weekend.
"Until yesterday we thought he would be available but now the game is getting closer I don't have the same optimism.
"He didn't train with the group so it's probable that he won't play.
"(Kalvin) Phillips can play as a centre back or Aapo Halme is another possibility - this is two possibilities.
Bielsa added: "Also for (Peacock) Farrell it will be difficult for him to play because yesterday at the end of the training session he had a problem with his knee and he probably won't be able to play. So probably Will (Huffer) or Kamil (Miazek) will play.
Leeds could ask the EFL for special dispensation to sign an emergency goalkeeper in the absence of both Peacock-Farrell and Blackman.
"And I can't tell you anything about the possibility of bringing someone in.
"I don't have any news about the possibility to bring in someone in January or maybe before."
Asked how close it was between Miazek and Huffer and who would start, Bielsa added: "I haven't made a decision yet."
Defensively, United are already without both Luke Ayling and Gaetano Berardi with longer term injuries.