The Reds will look to continue their push for the title when they take on Tottenham at Anfield on Sunday.
Liverpool currently sit two points clear of Manchester City but have played a game more than Pep Guardiola’s side.
Alexander-Arnold was unavailable for England for their wins over the Czech Republic and Montenegro.
And Klopp is not 100 per cent whether the right-back will be fit to start against Spurs following a back injury.
He told the club’s website: “Trent still feels his back. We are not 100 per cent sure, so we have to watch him. Trent wants to [be] 100 per cent, but we have to see.
“It is a strange one, it’s not an obvious injury that you can say something is broke or whatever, it’s just a bit annoying actually that he cannot feel really free.
“For him, it was really important that he could do the rehab and not being in normal training all the time.
“Hopefully [between] tomorrow and Thursday he can be back in full training and then it should be fine.”
Klopp believes Shaqiri will be fine for the Tottenham game on Sunday though.
“[He is] good, much better,” said the boss. “Shaq, since a couple of weeks [ago], has had some problems with the groin.
“He trained, not how he could train, but was still in the squad and all that stuff because we didn’t have a lot of options.
“Now he feels better day by day and should be fine for the weekend.”
Liverpool welcome Tottenham to Anfield for the Premier League clash which kicks off at 4.30pm.
They could go into the match in second as City face Fulham at Craven Cottage in the first game of the weekend on Saturday.
And Liverpool legend Kenny Dalglish believes the side are progressing well under Klopp.
He said: “Whether you win the title or you finish second, or you get progress in winning the Champions League or you don’t, I think the positivity in and around the place is brilliant and I think we really are stepping forward and getting closer and closer.
“We’re closer this year than we were last year, so that’s the most important thing.
“In the Champions League we got to the final last year and lost to Real Madrid, so maybe they’ll say ‘you’re only at the quarter-final stage so that’s not really progress, you’ve not got to the final yet or are not winning it’, but when you compare the progress from last year, you need to win it.
“So if you don’t win it, is that not progress? I think it’s still progress.”
