Milner was among the starters in a strong Liverpool side that returned to action on Thursday night, but was forced off before the break with a hamstring issue.
The veteran immediately removed his captain’s armband as he motioned to come off, but in his post-match interview with Sky Sports, Klopp said his No. 7 was optimistic.
“Milly is convinced it’s only a little, little, little thing,” he explained.
“But he felt something and we just wanted to make sure it’s not getting worse.
“It’s something in the hamstring, I don’t know. We have to see.”
The manager added: “All the rest should be fine.”
“Trent was ill, like Ox was until yesterday. Virgil trained at the AXA today,” Klopp continued.
“All the others should be available apart from the long-term injuries.”
Ibrahima Konate will not be part of the squad, either, with the manager revealing that the France centre-back is not due back for training until next week.
Klopp did elaborate on Van Dijk in his post-match press conference, however, insisting that he “should be ready for Monday.”