But the 29-year-old England international could return before the end of the season, with Klopp suggesting Liverpool's fixture against Brighton May 13 as a possibility.
"Adam is here doing his fitness work. He's not injured anymore but he's not fit yet," Klopp said ahead of Saturday's visit of lowly Stoke City.
"We hope still that one or two games might be possible for him. We will see.
"There is no chance for the weekend, no chance for Wednesday and then it could be difficult [for Chelsea].
"Maybe possible for Brighton for Adam. We have to see."
The Champions League final will take place on May 26, nearly two weeks after the Brighton clash.