Alexander-Arnold was a part of the Three Lions squad that reached the semi-finals of this summer's competition in Russia.
Klopp has already effectively already ruled Jordan Henderson and Dejan Lovren out of Liverpool's Premier League opener with West Ham United on August 12 due to their involvement in the latter stages of the tournament.
Alexander-Arnold only featured once for his country in Russia, however, and Klopp has revealed that the 19-year-old will have a two-week holiday before potentially joining up with the squad.
"With Trent, I have a special agreement," Klopp told reporters. "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'.
"If you asked Trent, he would be good to join us in Evian (for their training camp). But I'm not sure I will do that. I want to have them desperately but the season is really long."
Liverpool will continue their preparations for the 2018-19 campaign with a friendly against Blackburn Rovers on Thursday night.