Klopp has already effectively already ruled Jordan Henderson and Dejan Lovren of the Premier League curtain raiser on August 12 given their involvement in the later stages of the competition.
Alexander-Arnold featured just once for the Three Lions and is clearly keen to be back in action as soon as possible.
And Klopp has told the media that the 19-year-old will have a two-week holiday before potentially joining up with the squad.
He said: “With Trent, I have a special agreement. He wanted to be in earlier as well. As he’s very young, I said ‘OK, have two weeks’ holiday and then we’ll speak and see’.