Captain Henderson has missed each of the club's last four matches with a niggling foot problem suffered during training, yet initially there appeared to be real hope that he might be able to return for the 228th edition of the Merseyside derby – providing there was suitable progress made during the international break.
Quizzed regarding the latest team news during a pre-game press conference held at Melwood on Friday, Klopp revealed his skipper had suffered a "little setback" and is still not in a position to return to training.
"Jordan suffered a little setback and he is not in team training until now," he was quoted as saying by Sky Sports. "When we were here last time I said I hoped he could be in training this week. But we have to wait for this."
Urging caution with regards to any premature comeback, the manager added: "It's only a question of time, unfortunately. There's nothing we can do. Sometimes the issue isn't big enough and if there was a little chance he could run he would. But we have to be careful and not take a risk. It's always too long with injuries. There's nothing else to do."
Absent since a 2-0 defeat to Hull City in early February due to a virus that was followed by a fresh hip issue, Sturridge's chances of featuring against Everton appeared to be significantly enhanced on Thursday when he was pictured back in training. He subsequently took to social media to declare that he was "working hard to help the team have a successful end to the season".
However, Klopp moved to quickly clarify that involvement and insist the injury-plagued striker will definitely not be involved this weekend.
"[Sturridge] has no chance. He was on the pitch with the rehab coach."
Fourth-place Liverpool are set to be without Adam Lallana for up to a month as the result of a thigh problem sustained on England duty, although Philippe Coutinho and Roberto Firmino are both fit. Owners Fenway Sports Group (FSG) sanctioned the use of a private jet to fly the attacking pair back from South America on Wednesday night after they helped Tite's Brazil become the first team to qualify for the 2018 World Cup. with victories over Uruguay and Paraguay.
"They are okay for this weekend," Klopp said. "We will see how fresh they are. The club did everything to bring them back as soon as possible. They had the most comfortable trip they could have had. They had success [with Brazil], both looked good. Very important for us."
Liverpool's long-term absentees, Adam Bogdan, Danny Ings and Ovie Ejaria, are all still out.