The Reds have been away in Dubai on a warm-weather training camp, with the rest coming at an ideal time for some of the squad to recuperate after a taxing last few months.
Whilst Dejan Lovren has returned to training, the Reds' worries at the back have continued with Alexander-Arnold and Gomez still missing from training.
Gomez, who has been out with a fractured ankle since the first week of December, was due to return to training just after Liverpool's win at the Amex over a fortnight ago.
Speaking after the trip to Dubai, Klopp explained the youngster has faced a setback in his recovery and he faces another “couple of weeks” on the sidelines.
“We have to wait. Obviously it was really unlucky in that situation,” he told the official website.
“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.”
It's more of the same for fellow defender Alexander-Arnold, who suffered a knee injury following Liverpool's 1-0 win at Brighton.
Klopp had previously claimed the youngster was “really close” to featuring against Crystal Palace, however he has now suggested the 20-year-old could miss the next three games.
“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,” he explained.
“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 percent [back] but until then, we have to see.”
There is good news regarding Wijnaldum, however. The Dutch international missed Liverpool's 4-3 win over Palace with a knee injury, but is set to resume training as normal.
“Gini is good, better. 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,” he said.
With Fabinho possibly filling in at right-back against Leicester with Alexander-Arnold out and Milner suspended, the hope will be Wijnaldum can be fit enough to take his place in midfield.