The Brazil international became the most expensive goalkeeper in history after joining the Premier League outfit in a £67m move earlier this week.
However, Alisson was left at home as the rest of his squad travelled to America, where they will face Borussia Dortmund, Manchester City and Manchester United in the International Champions Cup.
Klopp admitted that the 25-year-old was eager to turn out for his new club but added that the new recruit needs time to recover after representing Brazil at the World Cup.
"When I saw him at Melwood, he looked fit," Klopp is quoted by Sky Sports News as saying. "He's desperate to play. He wanted to stay, but it made absolutely no sense.
"He's had a long year. As Brazil number one, it was quite an intense year. The World Cup is not a tournament you only play a little bit, it was intense. So I sent him on holiday again.
"There will still be two games to play before West Ham and then West Ham is only the first game of the season, not the last one. So we will see."