The Croatian centre-half limped off with a hamstring problem in the first leg of the League Cup semi-final against Mark Hughes’ men on 5 January, which the Merseysiders won 1-0 at the Britannia.
Lovren rejoined his team-mates for a complete session on Sunday, and could be on the bench for the reverse fixture on Tuesday night. Mamadou Sakho and Kolo Toure are likely to continue in the heart of defence.
"Dejan, after three weeks he trained yesterday, a complete session with the team," Klopp said at Melwood.
"It was good, but after three weeks we have to see. If nothing happens in the next 24 hours with Kolo or Mama then I think we should do it again because Steven [Caulker] can't play.
"That's not too good - you can buy players in January but if you're still in the cup you can't use them!"
Right-back Clyne received a knock to his knee in training and will be assessed late on to judge if he can play a part in the second leg. Jon Flanagan, who made his competitive comeback last week after being sidelined for 20 months, will deputise if the England international cannot feature. Klopp, however, prefers to ease the 23-year-old into action rather than giving him a full run-out in what should be a testing encounter.
"Clyney got a knock on the knee. He is a really tough boy, he is always available, but I think today it will not work for training," the manager added.
"We don't do too much, of course, but I think we should leave him out of training. We have to see what will happen overnight and make a decision but it's not too easy because we have only Flanno.
"We all love Flanno but he had a long time [out] and 90 minutes or more is maybe not the best thing. But if there's an opportunity we would like to try it.
"He is ready but of course it would be better if Clyney got fit."