Robertson is closing in on a return to team training, having spent the winter break in Dubai stepping up his recovery from shoulder surgery on the injury he sustained back in October.
Meanwhile, Szoboszlai has been out of action since New Year's Day after coming off in the 4-2 win over Newcastle and Alexander-Arnold became the Reds' biggest fitness concern – at least until news of Mohamed Salah's potential knock broke – when he sustained a knee injury in the FA Cup win over Arsenal.
Speaking in his pre-match press conference ahead of the game trip south to face Bournemouth this weekend, Klopp was asked about the progress of Liverpool's absent stars and insisted they are all 'close' to a return.
"Obviously, Trent can walk on the catwalk," the manager said, jokingly referring to his right back's appearance at a Milan fashion show during the break.
"They are all positive but not ready. They are all going in the right direction and we're getting closer and closer.
"Some of them might be part of team training next week. "For the Bournemouth game I don't expect anybody back. After Bournemouth and maybe for Fulham, we will see how they do but they are all close.
"Trent [is] close, Dom close, Robbo close. All going in the right direction but for the weekend's game, no."
Liverpool appear set to be without as many as ten first-team players for the clash against Bournemouth.
While Salah was already out of contention for the tie due to his participation in Egypt's Africa Cup of Nations' campaign, his injury scare in Thursday's draw with Ghana provides fresh concerns for Klopp.
Discussing his No. 11's potential knock, Klopp said: "We don't know anything. I spoke last night with him and how it is with his injury and further assessment. That's what they are doing now. And we will know more.
"At that moment, [it was] a shock ... [he] couldn't see that like he was hit by something high intense. You have these hamstring injuries in different ways but he felt it and we know how rarely Mo goes off, so it is definitely something but we will see. I don't have any more information."
He added: "There will be an ultrasound and MRI and then we will see."