The defender sustained a lower leg fracture during the 3-1 win at Burnley on December 5, forcing him to sit out the 10 fixtures that have followed since as he began a rehabilitation programme at Melwood.
Klopp told Liverpoolfc.com: “We have to wait. Obviously it was really unlucky in that situation. The injury is not like Trent or Gini where you know ‘that’s the only thing’. It could have been like that, but then more and more we found out it’s a more serious thing.
“We have to wait, for sure, a couple of weeks. We will see, it is difficult to judge in the moment.
“We thought three weeks ago he would be closer and then we had to make another diagnosis in which we saw that it didn’t work out so far as we wanted, that’s why he is still not in training or running on the pitch.”
The full-back sustained the issue during Liverpool’s 1-0 win at Brighton & Hove Albion on January 12 and subsequently missed the 4-3 victory against Crystal Palace last time out.
Asked for an update on Alexander-Arnold’s fitness, Klopp told Liverpoolfc.com: “He is better, much better, but we have to see. It needs to be stable – and in the moment it is stable and it’s about the pain.
“Everyone knows how desperate Trent is to play; he can ignore pretty much everything. That he played that game at Brighton was sensational, to be honest. It’s unbelievable. The same for Gini, who got a little injury early and it was very painful. Adrenaline is obviously really hard stuff and gives you the opportunity to grow a bit in the game, so they did.
“It will not be long [for Trent], but is he ready for Leicester? I don’t know, we will find out. Then it’s West Ham and then Bournemouth. After that he will be 100 per cent [back] but until then, we have to see.”
Like Alexander-Arnold, Georginio Wijnaldum also picked up a knock to the knee at the Amex and sat out the clash with Palace at Anfield.
“Gini is good, better,” Klopp added. “The plan is that he will have one session today and then we have to see how he reacts on that. Hopefully we can build from that point.”
Jürgen Klopp provided a positive update on the fitness of several players ahead of Liverpool’s return to action against Leicester City at Anfield on Wednesday night.
The manager confirmed Virgil van Dijk has resumed training following illness, while Georginio Wijnaldum is also back in contention after a knee issue.
Elsewhere, Fabinho is set to join his teammates in Tuesday evening’s workout at Melwood; however, Trent Alexander-Arnold will not be ready to face the Foxes.
Klopp said: “Virg was a little bit ill, but he trained yesterday and will train today, so we will see.
“Dejan [Lovren] is fine, Gini trained [and] Fabinho will train today.
“Trent is getting closer and closer and it all looks very positive, but he will not be ready for tomorrow.”
Gomez merely a routine operation designed to speed up the healing process, so not expected to set his return back any further. No timescale yet until results know, but could be back by (early) March if goes well. #LFC
Scotland have not given up hope that Andy Robertson will be available for Thursday's opening Euro 2020 qualifier in Kazakhstan.
Scotland captain Andy Robertson is out of Thursday's Euro 2020 qualifier against Kazakhstan.
The Liverpool full-back had met with the squad in Glasgow, but did not make the flight to Kazakhstan after being advised to have a dental operation.
But he has not yet been ruled out of the San Marino game three days later.