Klopp told reporters at Melwood on Friday that the club were assessing Sturridge’s injury “day by day.”
“I spoke a few minutes ago with him, it’s not much better,” he said.
“With Daniel’s injury we have to see day by day.
“If he can train tomorrow completely normal, then he is an option.
“Not as a starter, but he is an option. But I have to wait for this.”
Klopp explained that “there is a little fluid inside [Sturridge’s knee],” and that the striker would require a scan on Friday afternoon.
The Liverpool manager gave no assurances that Sturridge would be included in his match-day squad against the Saints, with both Christian Benteke and Roberto Firmino vying for starting roles after recovering from their injury problems.
But the long-term fitness issues Sturridge has faced during his time at Liverpool will no doubt trouble the German, who also discussed how his strikers “will defend for sure.”
“They have to close spaces for us so the rest can defend easy,” he continued.
“If you do this in an intelligent way, it’s easy for the rest to defend, it’s easy for you to get the ball back.”
Whether an injury-hit Sturridge can adapt to this system remains to be seen.