The Portuguese has missed the Reds’ last eight games with a hamstring injury picked up at Man City in late November.
And, despite taking important steps towards a return this week, it does not seem that he will be back in time for the trip to Turf Moor.
Speaking directly after the 1-1 draw with Arsenal, Klopp said: “I don’t want to rule out anybody now, we will see.
“He didn’t train with the team yet, we have only one proper session so it will be a surprise. But maybe I will get a surprise. I don’t know.
“He didn’t train with the team but the session I saw was really intense, but I didn’t ask who will be available yet and the medical department will tell me now or [Sunday].”
After losing Kostas Tsimikas to a suspected broken collarbone against Arsenal and with Andy Robertson still out after shoulder surgery, Liverpool are enduring something of an injury crisis at left-back.
Klopp has suggested that Joe Gomez will continue to deputise there as he did against the Gunners, but admits he is unsure whether the Englishman can play every game of a hectic period.
He added: “We will see. Can Joey play all the games coming up now until I don’t know when Robbo will be back?
“Kostas is now definitely out for a while. I don’t know, we will have to see.
“I didn’t have time to think it through but somebody will play the position, I’m pretty sure.
“You have injuries sometimes and you accept all of them, but a broken collarbone is really bad because it just takes long.
“Same with what Robbo had, a different injury but it just takes long as well as we all know. We all know we need luck in these moments to get through.
“Now we have Joey there and let’s put him in cotton wool and make sure he’s ready for the game.”
Youngsters Luke Chambers, 19, and Calum Scanlon, 18, are Liverpool’s other immediate options at left-back.
