Clyne, the Reds' senior right-back, missed training sessions on Monday and Tuesday with an abdominal muscle injury that has forced him out of two games earlier this month.
The England international featured in Saturday's Premier League defeat to Swansea City at Anfield, but hasn't trained since due to discomfort.
That means he is a major doubt for Liverpool's EFL Cup semi-final second leg against his former club Southampton, in which Jürgen Klopp's side need to overturn a 1-0 deficit to reach the final.
If Clyne is ruled out, his Academy graduate teammate Alexander-Arnold will step in again for his third appearance within just 10 days.
Alexander-Arnold set to continue recent rise
The 18-year-old, who made his debut in the fourth round win over top-flight rivals Tottenham Hotspur in this competition in October, has made six appearances for the first-team since then.
That includes his first start in the league for Liverpool in mid-January, when he filled in for Clyne for the trip to Old Trafford to face Manchester United and fared well in a battling 1-1 draw.
The West Derby-born teenager has regularly impressed when given the opportunity at senior level and Klopp would have no hesitation in turning to him again for the visit of the Saints.
Prior to the weekend's defeat at Swansea, Alexander-Arnold said: "There are world-class players in the Premier League and week in, week out you’re going to be tested in different ways. Whether it’s in the air or people going at you one-v-one, you’re always going to be tested. That’s what I’ve got to be ready for if I’m chosen to play again."
Otherwise, the Reds boss is expected to name as full-strength a line-up as possible - with captain Jordan Henderson available despite a troubling heel issue and Philippe Coutinho also in the frame to start despite also missing training on Monday.
The Brazilian recovered to take a full part of Tuesday's session and fresh from signing a new five-year contract with the club, will look to help Liverpool book a second League Cup final in as many seasons on Wednesday.
Klopp facing tactical dilemma against Saints
Bar Clyne, Klopp has no other injury issues to contend with - although he must decide whether to utilise Adam Lallana in an advanced position on the right of a front three or from central midfield.
Lallana has been one of the club's stand-out performers this term and much of his best football has come from a deeper position. He hasn't been nearly as effective further forward when trying to replace top goalscorer Sadio Mane, who is at the Africa Cup of Nations with Senegal.
Though if Lallana plays in central midfield, Klopp will also need to decide whether Emre Can drops out or not having endured a disappointing season so far.
The young German, said to be stalling over the offer of a new contract from Liverpool as he feels he deserves a higher wage, has been ponderous and has struggled to exert the kind of influence he had on the team last season.
Lallana could replace Can in central midfield, allowing one of Divock Origi and Daniel Sturridge to fill in on the right-side of a three-pronged attack, though central midfielder Georginio Wijnaldum could be another alternative to play further forward.