The Egyptian picked up a hamstring injury at the Africa Cup of Nations last month and was subsequently sent back to Merseyside to undergo his treatment.
His country have since been knocked out of the tournament, meaning his full focus is now on making a return for his club ahead of the run-in.
Klopp confirmed that Salah is yet to return to training with his team-mates, but did joke about his No. 11’s determination to speed up the recovery process.
“[He is heading in the] right direction,” the boss revealed as he previewed Saturday’s visit of Burnley.
“We hope, but we don’t know, that he will be part of parts of training next week, but we have to see.
“He’s going through all the paces now but it’s positive, it’s either next week or the week after. If you ask him, it’s next week!”
Salah has not appeared for the Reds since the victory over Newcastle at Anfield on New Year’s Day.
He departed for his international commitments immediately after the 4-2 win over Eddie Howe’s side, with the setback halting his return to Premier League action.
There have been mixed reports regarding the timeline for his comeback, with his absence from Thursday’s training providing clarity that it would not be imminent.
Last week the 31-year-old shared footage of him back out on the grass at Kirkby, but the manager has since indicated that he will not join his peers until next week at the earliest.
While fans will be keen to see Salah back in a Liverpool shirt sooner rather than later, the other forwards haven’t struggled for goals in his absence.
The Reds have netted 19 times in seven outings since his departure to Ivory Coast, but his presence will no doubt provide an even bigger boost to the threat in front of goal.
Klopp will need all five of his senior attackers to be on song between now and May, with his side still firmly in the mix in all four competitions.