Milner remains sidelined following a calf injury earlier this month.
"Jordon Ibe has been back in training since yesterday," Klopp told reporters. "He was sick and had a few problems for nearly a week. We will have to see. Yesterday was completely normal training, but we’ll have to wait on how he reacts to this.
"Millie (James Milner) will start pitch sessions, not with the team but outside tomorrow. Then, he needs a week and should be available."
The German also confirmed Belgian forward Divock Origi is set to miss the trip to Sunderland.
"I cannot say too much about Divock because at this moment I do not have the results of the scan," Klopp said.
"If there is no miracle or something like this, then he is not available for the next game, so we have to find a solution for this."
Liverpool have scored four goals in five league games and are running out of options up front, with only Christian Benteke to lead the attack as striker Danny Ings is out for the rest of the season with a ligament injury.
Klopp said he expects a tough challenge from Sunderland despite their woeful run of form, and that Liverpool would not take the game lightly.
Sunderland are in 19th place in the Premier League table after 18 games and winless in four, following their comprehensive 4-1 defeat to Manchester City on Saturday.
"There is no reason in the mentality of the team to think, 'oh it is only Sunderland'," Klopp said. "I know them and nobody in the team is like this.
"Everybody can imagine what will happen at Sunderland. I think they will go back to the roots and we know what is waiting for us. We will be prepared."
(Reporting by Nayan Das in Bengaluru; editing by Amlan Chakraborty)
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