The Brazilian sustained an injury days before the Reds returned to action after the World Cup, but was expected to return to action against Brentford on January 2.
However, having yet to resume training, Klopp has now revealed that Firmino is still “not close” to returning to team training, having sustained an injury setback.
Firmino won’t be available against Brighton, with the Liverpool boss seemingly reluctant to place a timeframe on his return.
“In the first moment it was like a little injury, estimated 10 days – two weeks,” Klopp told reporters on Friday.
“He did the normal rehab stuff, all the experts told us what we could do.
“Then Bobby felt again, something. That kept him out for longer.
“I don’t know exactly when he will be back, he’s not close to team training.”
Nunez’s injury issue emerged on Thursday, with Klopp confirming the club are awaiting further details on the severity of the problem.
“If he can not train today then yes, that will rule him out,” Klopp said of Nunez’s chances of featuring at Brighton.
“We are waiting for information. It’s not a major one but it still kept him out of training. We have to wait for that.”
“Milly did big parts of training yesterday and will be in normal training today,” he added.
“Stefan will be back in training today. He got a knock on the hip bone that was quite uncomfortable but he will be back as well.”