Lallana has been absent since sustaining a muscle injury during last month's 1-0 defeat to Swansea City at the Liberty Stadium.
But, at his pre-match press conference, Klopp said of the attacker: "He is for sure an option for the squad, but an option for the first XI?
"I would think not in the moment, but maybe I can sleep twice before we play Southampton so maybe I will change my mind on this. We will see."
Klavan, meanwhile, has returned to training after a thigh strain, while Moreno is also in contention having overcome a small setback in his recovery from an ankle issue.
Jordan Henderson is unlikely to start both of the next two games, at St Mary's and the subsequent Champions League tie against FC Porto.
"I don't think that would make too much sense," Klopp said of the captain, who is regaining full fitness after more than a month out with a hamstring injury.
One man who will not be part of the Reds' squad on the south coast, however, is Joe Gomez.
The defender was running at Melwood on Friday, but the boss explained: "I don't think he has a chance for Sunday if they don't come in and say the running was that good!
"Porto, there's a chance. We will see."
As for the hosts, their sole injury concern is striker Charlie Austin, who will definitely miss out with a hamstring problem.
Saints boss Mauricio Pellegrino said: "We have nothing to report in terms of injuries, which is good but we will wait until tomorrow.
"There is just Charlie at the moment who is outside of the squad but the rest of the team are ready."