The England Under-21s international came back from the recent break carrying an injury and played no part in the thrashing of Watford on Saturday.
There was thought to be hope of Jones shaking off the issue in time to face Atletico this week, but Klopp has conceded that the midfielder will not make the cut.
Speaking at his pre-match press conference, Klopp said: "Unfortunately Curtis was only with us in the warming up and will be here in Liverpool to hopefully make the final steps to full training.
"Today he did only warming up and then did his stuff, but still individual training and we decided to leave him here to continue that. And then hopefully he is ready for United."