The Reds boss spoke ahead of Saturday’s Premier League meeting with Burnley on the Egyptian winger’s bid to recover from a hamstring injury which has kept him out for almost a month.
Suffered while playing for Egypt at the Africa Cup of Nations, Salah returned to Merseyside for treatment and is expected to make a step up in his recovery at some point in February.
When quizzed by reporters on the 31-year-old, Klopp said his player was moving in the “right direction”.
“We hope - but we don’t know - that he can be part of parts of training next week,” he stated.
“But we’ll have to see, he’s going through it now. But it’s possible. It’s either next week or the week after - if you ask him, it’s next week.”
Following his country’s exit from AFCON, the handling of Salah’s injury was criticised by the country’s all-time top scorer Hossam Hassan, who has since been named the new Egypt manager.
Liverpool will be without Salah, as well as Thiago Alcantara and Dominik Szoboszlai, for the visit of Burnley this weekend.