The Brazilian has been out of the side since the defeat against Man City, missing the last three games with a muscle injury.
He had been considered a half-chance of featuring in the Merseyside derby but having not returned to training that was soon scuppered, as it will once more for the trip to Sheffield United.
Fabinho has not yet featured in team training since his point of injury and with just two days until the trip to South Yorkshire, it will likely be too soon for the No. 3 as Klopp revealed he is only now returning to training.
“Fab not yet with the team, that can happen I think tomorrow – if I’m 100 percent right. He will have his first session with the team,” he told reporters.
“And same for James Milner, that’s it.”
The good news is that Diogo Jota is to be included in the matchday squad after looking “very good” on his training return.
The injury crisis at Liverpool is best summarised by having all three senior centre-backs you started with the season out for the season and the two midfield back-ups both in the treatment room.