It was initially stated by the national team that Salah, 31, would sit out two games before he appeared before the press on Sunday to insist his country can win AFCON even in his absence.
But Liverpool boss Klopp has now poured doubt on his ability to play again at the tournament.
Only if Egypt reach the final and Salah responds well to treatment will he be released to feature, the German said after the 4-0 win over Bournemouth on Sunday.
He stated: "That's the plan. I think everybody sees that it makes sense to [do his rehabilitation] with us."
Asked if the player could return to AFCON, Klopp added: "If he is fit before the final, then probably, yes."
Salah refused to go into detail about his injury when facing questions from the media earlier in the day.
He said: "I am happy to be here, my injury is still there but the most important thing is to speak about the game. We have great players, a great team and we just need to fight and see what is going to happen.
"We have great players and these are the best 20 players in Egypt, so we need to play our game with courage and confidence and I believe we are going to win the game.
"I would love to win [AFCON], absolutely. I've won everything possible [with Liverpool] but not this one, yet. I believe it will happen, everything I believe I achieve, so it will happen. Sooner or later it will happen.”