The 25-year-old picked up a knee injury in the Reds' 2-0 FA Cup win at Arsenal on January 7 and was expected to be sidelined for 'a few weeks.'
However, Klopp confirmed the Liverpool vice-captain is closing in on a return to action but will not be risked for Saturday's trip to Bournemouth or the Carabao Cup semi-final second leg at Fulham on Wednesday.
Alexander-Arnold was pictured in Milan this week, modelling at the Dolce & Gabbana Fall 2024 Men's Show.
And Klopp couldn't resist a playful dig at the star while updating reporters on his side's injury absentees.
"Trent can walk on the catwalk! After Fulham we will see," Klopp said in his press conference on Friday.
Read more on Liverpool
In-form Dominic Solanke looks to shoot down old club Liverpool but Reds are comeback kings
Liverpool fans will love Hull boss' verdict on Carvalho after making surprise move
"Trent is close, Dom [Szoboszlai] close, Robbo [Andy Robertson] close. All going in the right direction but not for the weekend's game."
Alexander-Arnold's availability will be a welcome return for Klopp who learned of Mohamed Salah's hamstring injury at the Africa Cup of Nations on Thursday.
The England international was in sensational form before picking up the injury having registered none assists for the Reds across all competitions this season.
He has also netted twice with both goals coming in the Premier League and Klopp will hope there will be no further complications ahead of a crucial period of fixtures in the race for this season's title.
Most read in Football
Arsenal star Emile Smith Rowe targeted by London rivals in surprise January loan transfer
Henderson has already broken Ajax record and overtaken legends within 24 hours of transfer
Klopp 'shocked' by Salah injury as Liverpool boss offers update after worrying AFCON blow
Spurs fans delighted at viral video as club close in on transfer for Norway starlet Nusa
League leaders Liverpool will hope to banish memories of last season's disappointing 1-0 defeat when they head to Bournemouth on Sunday.
Liverpool's next two league fixtures see Chelsea visit Anfield before a trip to the Emirates to face title rivals Arsenal.
Simon Jordan explains why Pep Guardiola is not the best manager in the Premier League and how it is actually Jurgen Klopp