The 33-year-old midfielder ended his 12-year stay Anfield this summer, joining the Saudi Pro League side in a controversial £12m move.
Henderson has since given an interview with The Athletic in which he discussed all aspects of the transfer from the manner of his Liverpool exit, to the issues surrounding how the move squares with his previous advocacy of LGBTQ+ issues.
One of the most talked about quotes from the interview came when Henderson suggested that he left Liverpool because he no longer felt wanted at the club he had captained since 2015.
He said: "If one of those people [the manager or owners] said to me, ‘Now we want you to stay’, then we wouldn’t be having this conversation.”
Asked about that quote at his Friday press conference, Klopp confirmed that he told Henderson he couldn't guarantee him regular game time, but insisted he did want the England midfielder to stay.
Klopp said: "Hendo said the truth, in all departments, that’s how it was.
"We had our talks and I told Hendo I wanted him to stay but we had to talk in these conversations about the possibility of not playing regularly, I told him we bring in players and stuff like this."
Klopp also suggested that Henderson's driven personality type and need to play regularly made him interpret the changing squad situation in a more negative way.
He said: "Because Hendo is a fantastic player, I will love him forever, super guy, but he’s not great when he’s not playing, let me say it like that. Milly was like that when I arrived here and Lucas Leiva was like this.
"You always thought they are great guys but then the moment they see the line-up and they are not involved they turn into Jekyll and Hyde, it’s unbelievable.
"That’s Hendo’s problem, so you have to talk about that.
"He was my captain for seven-and-a-half years, so I had to talk about that because I don’t want to wake up one morning and need to lock horns with each other because he thought he would start and I tell him he isn’t.
"Obviously [for] Hendo that meant, ‘Okay, he doesn’t want me here’. I understand it 100 percent but we clarified that.
"What he said is that if I would have told him: ‘Hendo, stay here, you will be the main man in midfield’, he would have stayed, that’s the truth. But I couldn’t say that, as much as I wanted him to stay, I couldn’t say that. So that’s why it was better that Hendo moved on."
Klopp also insisted that despite Henderson's exit, he holds no grudges towards the player.
“There’s not a bit of bad blood or whatever," Klopp added. "He is the captain of the most successful team this club saw in the Premier League era and rightly so, he’s a sensational player.
“I wish him only the best and, when he comes here, from my point of view he gets a real farewell, everything, there’s nothing to misunderstand from that point of view.”