The England international remains unavailable for Liverpool's upcoming clashes with Leicester City and Burnley in less than 48 hours but could avoid the month-long lay-off that some reports suggested he could face earlier this week.
Klopp wary to pencil in Henderson return
Asked for an update on when he expected to be without his skipper until, Klopp replied: "There is always a prognosis but it depends on the healing process and if the player is a quick healer or not. [There are] big differences between individuals."
The German revealed that Henderson will start "running outside today" and insisted "which pace and whatever" they "will see."
"But he is on a good way," he continued, declaring that he does not want to "say any date" because it might "put pressure on him" which Klopp feels the midfielder "really doesn't need."
He added: " And on the other side it would look like we would not have the player for the next six to eight weeks and that's not true at all. We have to wait. Hendo, I think is a rather quick healer. He is on a good way and is desperate to be back on the pitch, so hopefully [his absence is] not too long."
Moreno could return for Manchester City
The Reds are also without left-back Alberto Moreno who has missed all of Liverpool's last five games with an ankle injury sustained against Spartak Moscow at the start of December.
But Klopp has suggested the Spaniard will be available after the nine-day break following an FA Cup third-round tie with Everton and could come into contention for an Anfield showdown with league leaders Manchester City on January 14.
The manager labelled Moreno as "probably the quickest healer in the squad" but insisted he is still "not sure" as to when the full-back will be available again.
He ruled the 25-year-old out of the next two games against Leicester and Burnley but said: "I think I should have to involve the third game [against Everton] as well."
Klopp noted the break of "around about nine days" between the Merseyside derby and the visit of champions-elect City and insisted the visit of Pep Guardiola's charges "could be the first [match]" back for Moreno.