Liverpool midfielder Thiago Alcantara is available for Wednesday's Champions League Group A opener against Napoli after returning to training following injury.
But another midfielder, Jordan Henderson, is out after suffering a hamstring injury in last week's win over Newcastle United.
The return of Spain international Thiago, who has not played since the opening day of the Premier League season, is a boost for Klopp who has had several players absent in the opening weeks of the campaign.
"Thiago, back in training, second day today. [It] means he is ready; for how long, we will see," said Klopp.
The German said Henderson, however, would not be back until after this month's international break.
Brazilian Arthur Melo, signed on loan from Juventus last week, could play some part in the game, said Klopp.
"He needs football and training. He was not in team training for a while. Can he play minutes? Yes. Should he play a full game? No," he said.
Liverpool have lost both their previous meetings in Naples in the Champions League.
Klopp's side were runners-up in last season's competition, losing to Real Madrid in the final in Paris.