Henderson was not selected among the substitutes for Liverpool's final pre-season friendly with Blackpool on Sunday (AEST) as he continues his recovery from a knee injury.
However, manager Klopp provided a positive update on Henderson, whom he anticipates will take part in a full session in the coming days.
Liverpool begins its defence of the Premier League title against promoted Leeds United next weekend.
Explaining Henderson's absence from the clash with the League One club, Klopp said: "Obviously Hendo was desperate to play a few minutes today as well, but it makes no real sense because he had to do an important session today for him.
"If he would have played today, 10 minutes or so would have probably been okay. But that makes no sense.
"So that was not possible, but he trained in big parts of this week and will probably join full team training next Tuesday.
"Timing-wise, not perfect that he cannot play today, but can train a few days later fully. But that's how it is.
"We will see how he develops, [there are] a few days until Leeds, how the boys come back from the national teams.
"A lot of open questions still, but a few hopefully we can answer today."