The Reds captain has not featured since February 11, having been sidelined with a foot injury picked up in training, and has missed his side's last eight games.
With five fixtures left in the 2016-17 campaign, it had been hoped that the 26-year-old would play a part in the club's home stretch, but Klopp could not elaborate further on his player's fitness.
"Still nothing new [on Henderson]. I don't know, we will see," the German coach told reporters on Thursday. "In this moment he cannot really train. We have to wait for this moment, if there's something else to say about this I would say.
"We are in intense talks with different departments, but we have to wait. He is already not patient anymore. It's not cool. He looks really healthy actually, but he cannot play football, that's the situation."
Liverpool's battle to secure a Champions League spot continues on Sunday when Sam Allardyce's Crystal Palace come to Anfield.