"Daniel is becoming closer and closer, he can train seven or eight times in a row," Klopp told a news conference on Wednesday.
"That will help him and us. My decision you will see tomorrow. He can train without problems.
"We have to try to bring him into a situation. A good moment, for a few minutes or more, we’ll see."
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Sturridge has suffered badly with injury over the past two seasons. He started only seven league games last season, the last of them in March, then had hip surgery.
After taking part in only three matches this season, all under previous manager Brendan Rodgers, he hurt a knee in training and has not played since.
Christian Benteke, a late substitute in the outstanding 4-1 Premier League win at Manchester City last weekend, could also appear in a game in which victory will qualify Liverpool for the next stage of the competition.
They drew their first three matches in Group B 1-1, starting with the away game against Bordeaux, then won 1-0 away to Rubin Kazan to stand second in the table two points behind leaders Sion.
"We are in a good way to play better at home, we are creating chances," said Klopp, who does not want supporters to make too much of having lost the last game at Anfield 2-1 to Crystal Palace.
"We should not make a bigger point of (home form) than it is, what we need to do is develop the performance," he said.
"(There were) brilliant moments against Man City but we were far away from perfect. Many things we can do better when we train more often together."
Croatian defender Dejan Lovren told the news conference that the players have "started to believe in ourselves since Klopp came in".
"It's a great pleasure to play under Juergen," he added.
"We know what he achieved with Dortmund before. He has made great changes here."
The manager was not keen, however, that those changes should be made public.
"I don’t want players to speak about our training and what we do, because it’s our training," Klopp said.
(Reporting by Steve Tongue; Editing by Rex Gowar)
