Vice-captain Milner returns from a one-game suspension, served for the 1-1 draw against Leicester City, as the leaders journey to the London Stadium.
The match comes too soon for Alexander-Arnold, however – the Reds right-back’s recovery is continuing at Melwood, confirmed Jürgen Klopp.
“Trent is getting better and better and better,” said the manager at his pre-match press conference. “He is really close and I hope he is in full training next week, but not for Monday.”
Joe Gomez remains sidelined following the lower leg fracture he sustained at Burnley in December and will undergo surgery to assist his recovery.
Having filled in at right-back against Leicester, Jordan Henderson is in line to make his 300th Premier League appearance – including 71 for Sunderland – on Monday.
Liverpool eased to a 4-0 win over the Hammers in their opening game of the season but Klopp warned that his side will face a much-improved outfit in the reverse fixture.
“Then, they still had a couple of weeks where they really had to find [something] together,” said the boss when asked for his assessment of the opposition.
“But they did it and now they are one of the strongest teams. It was a really bad start; since then they are nearly a top-six side. And that’s what we should expect.”
West Ham will give Marko Arnautovic every chance to prove his fitness for the game after he suffered a foot injury against Wolverhampton Wanderers last time out.
“We are not sure about Marko,” explained Hammers manager Manuel Pellegrini at his pre-match press conference on Friday afternoon.
“We need to see the development and the pain in his foot. We have 72 hours more to see if he will be able to play. It’s more a question for the doctor.”
Goalkeeper Lukasz Fabianski is available for Liverpool’s visit and Aaron Cresswell is in contention, but Samir Nasri is ruled out.
Pellegrini added: “Fabianski will be OK. He didn’t work today 100 per cent but I think he will be able to work normally tomorrow. Aaron Cresswell is getting better, but Samir Nasri needs one week more.”
Last time out
Wolverhampton Wanderers v West Ham United (January 29): Fabianski, Zabaleta, Ogbonna, Diop, Masuaku, Anderson, Snodgrass, Noble, Rice, Arnautovic, Antonio.
Liverpool v Leicester City (January 30): Alisson, Henderson, Matip, Van Dijk, Robertson, Wijnaldum, Keita, Shaqiri, Mane, Salah, Firmino.