The England protector, 23, experienced the injury during Wednesday's Premier League succeed at Arsenal.
It implies he will likewise miss England's friendlies against Switzerland and Ivory Coast one week from now.
"Trent is out with a hamstring, so he can't be important for England as well," said Klopp.
"Not uplifting news, we will perceive the way lengthy that takes."
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Joe Gomez and veteran James Milner are the reasonable contender to supplant Alexander-Arnold, yet Klopp concedes neither have the equivalent range of abilities as the England global.
"Obviously to supplant Trent is troublesome yet conceivable," added Klopp, whose side travel to Nottingham Forest in the FA Cup quarter-last on Sunday.
"I don't have a clue about any player who plays like Trent, so its challenging to track down a balanced substitution.
"We have Milly [Milner], Joe, hypothetically we can change the framework too, these sort of things. So we have several choices.
"Whenever you examine the previous when Milly has needed to move forward he has done extraordinarily well. What's more, while perhaps not perhaps we have a youthful arrangement."
Klopp's side host Watford in their first Premier League game back after the worldwide break on 2 April, before an essential outing to title rivals Manchester City the next week, either side of the main leg of their Champions League quarter-last against Benfica.
The Merseysiders are presently second in the Premier League, one point behind City.
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