Forward Origi suffered cramp during the Reds’ midweek win at West Ham United, while midfielder Lallana has missed their last three games due to a virus.
Both, though, are likely to be available as the Premier League leaders seek to extend their advantage at the top of the table to 22 points.
“Adam trained normally, Divock was cramp,” Jürgen Klopp said, during Friday’s pre-match press conference.
“He didn’t train yesterday because it was not a day for him to train. But I heard nothing else so he should be in training today.”
James Milner (muscle) and Xherdan Shaqiri (calf) are not yet fit, although Klopp hopes the duo will be in contention for selection again after the Saints clash.
Sadio Mane (muscle) is unlikely to face Ralph Hasenhuttl’s side.
Stuart Armstrong will miss out for Southampton, while Cedric Soares has joined Arsenal on loan.
Hasenhuttl told the media on Thursday: “Cedric is out and Stuart is injured and cannot train at the moment. It’ll take two to three weeks, I think, until he’s back in the team. It’s not the worst but he has a little bit of a problem with his hip muscles so he is out.”
Otherwise, the visitors will be at full strength at Anfield.
Hasenhuttl continued: “The rest look good. Yan Valery is back in training since the beginning of the week and Jannik Vestergaard is back from his concussion and also training. Everyone is fit.”
However, Kyle Walker-Peters, who moved to Saints on loan from Tottenham Hotspur on Wednesday, will not be involved this weekend.
Last match (Premier League)
West Ham United 0-2 Liverpool (January 29): Alisson, Alexander-Arnold, Gomez, Van Dijk, Robertson, Henderson, Wijnaldum, Oxlade-Chamberlain, Origi, Salah, Firmino.
Crystal Palace 0-2 Southampton (January 21): McCarthy, Soares, Stephens, Vestergaard, Bertrand, Hojbjerg, Ward-Prowse, Armstrong, Redmond, Long, Obafemi.