The Reds have not been in the favour of fortune so far this season, with a ridiculously intense schedule – and some particularly reckless challenges – depriving Klopp of a number of key players.
Most prominently, this comes at centre-back, with Virgil van Dijk likely to miss the rest of the season, Joel Matip struggling with ongoing issues and Fabinho the latest to be sidelined with a hamstring problem.
Williams, Phillips and Koumetio are all vying for a place alongside Gomez, with Sepp van den Berg seemingly not under consideration, and all three present an interesting case for a starting role.
So who is best suited, and why? Here, we run through the pros and cons.
Senior appearances: Kidderminster Harriers (29), Liverpool (four)
The obvious, and perhaps most suitable, choice is Williams; he has already stepped in twice in the Champions League, and is on a high after a dream week with both the first team and the under-23s.
Klopp was full of praise for the 19-year-old’s performance coming off the bench to replace Fabinho in the 2-0 win over Midtjylland, while he also stood out in the League Cup clashes with Lincoln and Arsenal earlier in the season.
An unexpected rise from non-league loanee last season to Champions League stand-in this highlights the gamble Klopp may be making in keeping faith with Williams, however.
He remains a raw talent, who has the aerial and technical quality to suggest he could be a long-term option for the Reds, but it has been mentioned a number of times that the occasion can still affect him.
“The only problem we, unfortunately, have now is we have four days until the West Ham game,” Klopp said after Williams’ most significant outing to date, against Midtjylland.
“And you will make a story of him, then he has to prove that he can deal with that as well, because before everything was calm around him.”
There is a likelihood that Alisson and Gomez will need to talk Williams through games if he is relied upon in the absence of Fabinho and Matip, but the early signs are that he can excel with an extended run of games.
VERDICT: The most likely, and most deserving, starter.
Senior appearances: None
Koumetio, or Billy the Kid as Klopp has affectionately nicknamed him, would likely have been given the opportunities enjoyed by Williams in recent weeks were it not for a series of minor injuries.
The Frenchman was a surprise inclusion in Liverpool’s squad for pre-season, and though still turning out for the under-18s in their 3-1 loss to Man City in September, looked set for a permanent role with the first team.
Instead, a spell on the sidelines has seen Koumetio drop down the pecking order, and yet to return to full training, the 17-year-old is unlikely to be risked any time soon.
But despite Williams making big steps in recent weeks, it can certainly be argued Koumetio has higher upside in the long-term; he is already built like a senior centre-back, and plays with a finesse that belies his young years.
It is likely that Koumetio will have made strides if he had remained fit over the past month, but at this stage, the error that hampered his first start for the club in the 7-2 win over Blackpool in pre-season serves as a reminder that patience is required.
Perhaps, if injuries to the likes of Matip and Fabinho persist, Koumetio will be called upon for the FA Cup in January, but as of now, it seems too early to throw a half-fit teenager in at the deep end.
VERDICT: Still too early in his development, particularly after injury.
Senior appearances: Stuttgart (22), Liverpool (one)
An out-of-position Jordan Henderson may be the true wild card, but having failed to secure a move away in the transfer window, Phillips’ availability cannot be overlooked.
Out of the three, Phillips is by far the most experienced player: he is four years older than Williams, and two months older than Gomez even, and a campaign on loan with Stuttgart in the 2.Bundesliga last season gave him a genuine taste of senior football.
Like Koumetio, he has endured fitness problems of late, but having returned to Melwood earlier in October has been a regular part of Klopp’s squad in recent weeks.
Given he is not in Liverpool’s Champions League squad, having not been registered in anticipation of a late move to the Football League, it can be argued that Phillips should take Williams’ place in the league to preserve the teenager’s fitness.
But while he is a more hardened senior centre-back, Phillips’ time at Stuttgart highlighted the limitations that led to him not featuring in Klopp’s initial plans for the campaign.
A lack of pace is the key issue, while he is more suited to a simple approach in possession, which would likely require more of a tactical rethink than allowing Williams to acclimatise to the existing system.
All signs point to Williams as Klopp’s go-to option in this early-season crisis, but Phillips remains a dependable centre-back if more rotation is needed.
VERDICT: A useful option if Klopp needs to rotate Gomez and Williams.