But the 26-year-old has been sidelined since mid-December with an injury that the club initially described as a “sore knee” and have failed to provide an update on after that.
It is clear that it is a more serious issue for the Belgian, who is yet to even return to light training having now missed seven games in all competitions.
There have been suggestions of interest in Origi this month, with three clubs in Serie A – believed to be Lazio, Juventus and AC Milan – linked along with Newcastle and Fenerbahce.
With Newcastle completing a £25 million deal for Chris Wood on Thursday morning, it is safe to assume that can now be ruled out.
And speaking ahead of a League Cup semi-final that Origi would almost certainly have started were he fit, Klopp cast doubt over a January exit.
“Div is not available. Div didn’t train, still injured, still in recovery, so he cannot help us in this moment,” he said.
“But I don’t see any kind of scenario [where he leaves in January].
“Pretty much everything can happen in life, but in this moment I would say he will be here.
“And hopefully fit soon! Because we actually could use him quite well now.”
What does this mean for Origi?
It has been a relatively strong season for Liverpool’s No. 27 so far, with five goals and two assists in 10 outings, for an average of a goal or assist every 56 minutes.
He has emerged as a valuable squad option again, and as Klopp attests, he would have been particularly useful during this January run with a dearth of senior forwards.
But there is no avoiding the sense that, after eight years with the club, Origi is into the final months of his time on Merseyside.
An expiring contract makes that a near-certainty, though claims that he could sign a pre-contract with a side overseas – namely one in Serie A – are muddied by an automatic extension clause if he meets a certain number of starts.
As it stands, Origi will not meet that target and will leave on a free transfer at the end of the campaign – a bona fide Liverpool legend, albeit one whose contributions have been sparse.
But Klopp’s acceptance that “pretty much everything can happen in life” does leave the door ajar when it comes to a mid-season exit – as the club are hardly going to turn down a big-money offer.