The Reds host the Baggies at Anfield this weekend as they look to consolidate their four-point lead over Leicester City at the summit of the Premier League.
Thiago is "not too far away" from returning to action but the Spaniard remains sidelined. Milner and Shaqiri, however, could be involved against West Brom, with Klopp insisting "it looks good."
“Thiago made his first steps back towards team training. He is not involved in the full session but makes good steps,” Klopp said.
“After, unfortunately, the long time he is out now, we cannot and will not rush it.
“The other guys are further, or closer. Shaq trained really good and Millie, yesterday full session, today then a little bit adapted.
“It is a new situation for us; we have still two more training days until we have to make decisions.
“It looks good, but I don’t know. Thiago will not be involved, he has to first be in full training sessions and then we start thinking about it. He is not too far away, I hope.”
Mane's goalscoring efforts
While goals haven't come freely of late for the Senegal international, Klopp insists he isn't concerned about his lack of scoring, with the boss delighted with his all-round contributions.
"Honestly, I would have lost everything if I had to bet on it, how many goals Sadio Mane scored in the last 10 Premier League games," Klopp said. "One would have been the last [option] I would have chosen, I had no idea that he only scored once.
"A second ago we spoke about the best goal difference that we have in the league and then I realise that one of our best players, one of the best players in the world, didn’t score for a while… I could just [say], ‘Who cares?!’
"He played exceptionally well, he is in really good shape, he is unbelievably difficult to defend. If Sadio has the ball, as an opponent you need to put pretty much two or three players on that side and that opens up for us a lot of things.
"I was not concerned but scoring then is, for the boys, obviously really important. Bobby obviously liked it – two weeks ago we spoke about him and since then he scored three or four goals.
"So now if Sadio starts scoring now again I have absolutely no problem with it but it was not about his performances, the performances were really, really good."
Being top at Christmas
The reigning Premier League champions lead the pack at Christmas for the third consecutive year, despite a sprinkle of sub-par results, especially earlier in the season.
Long-term injuries to Virgil van Dijk and Joe Gomez, amongst several other knocks to key members of the squad, had raised the prospect of the Reds falling off this season. But Klopp's side have instead shown remarkable grit to storm four points clear at the top of the table.
But Klopp downplayed the Reds' start so far as he insisted there is still a long way to go in the season, citing the titleless 2017-18 season when Liverpool topped the festive table.
"Obviously it means you are not automatically champions in May when you are the Christmas leader or whatever, otherwise we would have won the league two times before!" Klopp said.
"Look, it’s the best position you can be in at the moment but that’s it, that’s all. We know how tough it was, how tough it is, how tough it will be. We didn’t even play half of the season but [that] probably usually happens around about this time.
"It’s nice, nothing else, and two years ago when we didn’t win the league after being top at Christmas it was not about a lack of focus or whatever. It was just the quality of the opponents and this quality is still out there, so nothing really happened so far.
"We collected a few points and if you want to do something special this year then we have to collect even more until the end of the season and that’s what we try. That’s it."
An unknown and "tricky" test
The Reds' opponents parted ways with Slaven Bilic last week, with new boss Sam Allardyce taking charge of the Baggies at home to Aston Villa last weekend.
It was a disappointing maiden affair for the 66-year-old, who presided over a 3-0 defeat that saw the hosts with just 32% possession and one shot on target after a first-half red card for Jake Livermore.
But Klopp insisted it will be a "tricky" contest on Sunday, with the Reds lacking any concrete information on Allardyce's plans for his second game in charge.
"I would say they have a lot more information about us than we have about them... Sam only had a few days before the Aston Villa game and now he had a full week, that’s a big difference as well," Klopp said.
"Not a lot of changes for the first game he was in charge, but now obviously they have to replace Livermore. They could change system, they could do a lot.
"Most of the time when we prepare a game, we have to use the last three or four games they played before they face us and then we play them and they play a completely different way against us, because obviously with the football my boys played in the last couple of years a lot of people think to change a few things when they face us.
"So it’s always tricky, but we anyway do it, we do the analysis and we try to get as much information out of it as we can, but we never can be sure. So we focus mainly on the things we can influence and that’s it, pretty much.
"Hopefully we will have the ball a lot, if we have the ball a lot we have to create. If you create you have to do that together, if you lose the ball in these moments you have to be there for the counter-press, these kind of things.
"So yeah, I prefer knowing a lot about an opponent but most of the time I don’t know a lot because, how I said, they come to us and when they’ve played six times in a row with four in the back, they come to Liverpool and then they have five at the back all of a sudden. So we will see."
On the challenges of facing an Allardyce side, Klopp added: "What I expect is a tough opponent, it was always tough against Sam Allardyce teams.
"[They are] well organised, don’t make a big fuss of possession or whatever and in the situation West Brom are in anyway then it will be a proper fight.
"Sam is a proven specialist for organising teams for these kind of fights so we expect a tough game, obviously."
Watch everything Klopp had to say during his press conference above.