United currently have a total of 11 players sidelined with short or long-term injuries, though Sir Alex is hopeful a few of them will come through training on Friday.
Rio Ferdinand missed last weekend’s win over Arsenal with a recurrence of his back problem, while Phil Jones suffered an ankle injury and Nani hobbled off late on. Wayne Rooney, Patrice Evra and Michael Carrick also picked up knocks.
The champions were already missing Anderson, Tom Cleverley, Ashley Young, Michael Owen and long-term absentees Darren Fletcher and Nemanja Vidic.
"I can’t give you much of an update on injuries," Sir Alex said at his Carrington press conference on Friday.
"Hopefully we'll have two or three training this morning and we'll be better by tomorrow. It is not the best situation for us."
Sir Alex is confident his side will be able to handle a hostile atmosphere in Saturday’s fourth-round tie.
Much of the pre-match talk has centred around Evra’s return to Anfield, but his manager would rather focus on the football – though he admits he’d rather have been welcoming the Merseysiders to Old Trafford.
"I always think home draws make you favourite," Sir Alex said. "But it's a massive game for both clubs. There's a tremendous profile on it. There will be interest throughout the country.