The No.20 has been absent since picking up an injury in mid-October, though has recently returned to training with the Reds.
Liverpool are also waiting on Virgil van Dijk, Roberto Firmino and Arthur Melo ahead of the Everton meeting, while Thiago Alcantara is battling a hip flexor issue.
“The players are back in training, [but] still in different stages,” Klopp said during his pre-match media briefing.
“Diogo is the closest, he trains now normal already for two days, so another three days [of] training is possible for him. I think he is in contention for the squad, I would say, but we have to wait a little bit.
“Bobby next one, I don’t know, we have to see how that looks now, how he deals with training intensity [and] stuff like this and then we make a decision there.
“Virgil, I don’t think he is that close already, but we will work on that as well. Arthur, probably similar to Bobby, I would say.”
On Thiago, he added: “Yeah, Thiago has some problems. I know the problems, but I have to ask the medical department what I am allowed to say about it. Hip flexor, stuff like this, that’s it pretty much. He wasn’t able to train.”
Ibrahima Konate and long-term absentee Luis Diaz are set to miss the fixture, while Fabinho has been back in training after being absent against Wolverhampton Wanderers last weekend due to illness.
For Everton, Dominic Calvert-Lewin is “touch and go, at best”, according to manager Sean Dyche.
The striker continues to recover from a hamstring injury, which he picked up against Arsenal last weekend at Goodison Park.
“We’re still monitoring him,” Dyche said in his pre-match press conference. “It will be touch and go, at best, I would think. We’re hoping it settles down as quickly as possible.”
James Garner and Ben Godfrey have recently returned to training and could be involved, though Andros Townsend remains out.