Jordan Henderson and Naby Keita will miss Liverpool's Premier League clash against Arsenal on Saturday and are doubts for the Reds' Champions League trip to Red Star Belgrade.
Henderson has been sidelined with a hamstring problem he sustained during Liverpool's 1-0 win over Huddersfield Town on October 20.
The England midfielder missed the home victory over Red Star and last weekend's 4-1 triumph over Cardiff City, and he Klopp will not be rushing him back into action.
A similar complaint has also troubled Keita and, while he is closer to a return, Klopp does not expect either to feature in Liverpool's upcoming clashes.
"Hendo feels really good but it will probably be the start of next week when he will be back in training," Klopp told a media conference.
"Naby [will be back] at the end of this week, but that makes no difference [on his availability] really.
"In football, a not too serious injury takes still two, three or four weeks. You are lucky if you only have an injury like that, but that only means in the Premier League [you will miss] 20 games!
"They are completely on time, it's like we expected it. We didn't have to rush it – actually we couldn't, but there was no reason for trying it.
"If the next game would be next Friday then probably both would be fit, but the next game is on Saturday and the other one on Tuesday, so that could be a bit tight.”
There is better news on Mohammad Salah, though, with Klopp confirming the Egypt international will be able to feature against the Gunners despite a wrist problem that saw him wearing a protective glove earlier this week.
He added: "Mo is nothing serious, just an inflammation of the tendon.
"That’s pretty much all, it [the glove] was only for protection – the pictures you saw were only protection and it has no influence [on his availability]."
