The Reds welcome Burnley to Anfield this weekend, hoping to turn their poor recent form around.
Liverpool were on the receiving end of a 5-0 hammering off Manchester City last weekend and failed to see out the lead against Sevilla in the Champions League on Tuesday.
And Klopp provided injury updates on the sidelined trio, who have all been missing from the early season clashes.
“Ingsy is in training, Adam and Clyney are still too far away," he said.
“Maybe Adam can start running this week or beginning of next week.
"Clyney is improving a lot, I’m not sure about when it will be that he starts training completely normal.”
Ings has only managed 11 appearances since joining from Burnley.
Meanwhile, Lallana has been sidelined with a thigh injury he picked up in pre-season.
Clyne is expected to return in the New Year after picking up a back problem in a summer friendly.
One player who is set to be handed a start this weekend is Philippe Coutinho.
The Brazilian made his first appearance of the season against Sevilla in midweek, coming off the bench for the last 15 minutes.
The midfielder tried to leave the club in the summer after prolonged interest from Barcelona.
"Coutinho should be ready. I was really happy with how the crowd welcomed him, I don’t think anyone was 100% sure on this," Klopp added.
"I think as a Liverpool family, we were sensitive to it. For him it was good.
"So far he has trained outstandingly."
