Jürgen Klopp confirmed during his pre-match press conference that muscular injuries mean Milner and Keita are unavailable for the trip to London, along with Dejan Lovren (muscle) and Fabinho (ankle), who are set to begin training fully again next week.
Shaqiri, however, is in line to be in contention after a three-match absence due to a minor muscle issue, while Joel Matip is making positive progress following his lay-off due to a knee injury.
“James and Naby are not available. Both are muscle injuries, different and for different people, so we see how quick they will be,” the boss said on Friday.
“We really don’t have to put a timeframe on it because we don’t know it exactly. We will see, we are open and whenever they want to join us again, they can – or when the medical department gives the green light.
“For sure, not for this weekend, not for next week, but then we will see.
“Joel was not part of all parts of training [this week]. He was outside on the pitch, which looked really good, but then he had to do his own stuff again. Yesterday he was part of the first part of training.
“Shaq trained completely normal since he’s in. Dejan and Fabinho we expect to be back next week in full training.
“That’s obviously good. If that’s then early enough for the United game, I don’t know but we will see. They work really hard in the moment and they go really through the paces, so that’s good.”
Spurs will be without Harry Kane on Saturday after the striker joined their list of absentees with a hamstring injury.
Moussa Sissoko (knee), Hugo Lloris (elbow), Ben Davies (ankle) and Tanguy Ndombele (hip) are also sidelined, but Danny Rose has returned to training after his calf problem.
Mourinho, meanwhile, told the media that Tottenham will be up against ‘the best team in our competition’.
“They are the best team in our Premier League and of course it’s a big challenge for us to play against them,” he said.
When Klopp’s assertion that Liverpool must play ‘unpredictable’ football this weekend was put to Mourinho, he replied: “He can be unpredictable.
“He can play with Firmino as a No.9, he can play with Firmino as a No.10, he can play with Salah and Mane wide, he can play with Salah and Mane as strikers and Firmino dropping back, he can play Shaqiri and decide to change lots of things, he can play Origi.
“He can do so many things that he can be unpredictable, yes. It’s more difficult for somebody that plays against them exactly because they have the potential for that unpredictability.”
Last match (Premier League)
Southampton 1-0 Tottenham (January 1): Gazzaniga, Aurier, Alderweireld, Vertonghen, Sessegnon, Ndombele, Sissoko, Eriksen, Moura, Alli, Kane.
Liverpool 2-0 Sheffield United (January 2): Alisson, Alexander-Arnold, Gomez, Van Dijk, Robertson, Henderson, Milner, Wijnaldum, Mane, Salah, Firmino.