The Brazil international was the Merseyside outfit’s standout player in their League Cup final defeat at Wembley on Sunday afternoon.
Lucas excelled in an unorthodox centre-half role alongside first Mamadou Sakho and then Kolo Toure against Manchester City.
The Brazilian missed his spot-kick in Liverpool’s 3-1 penalty shootout defeat and Klopp revealed that the midfielder picked up an injury when he took his attempt to compound the 28-year-old’s misery.
“We have to wait for a few things, but it doesn’t look too good with Lucas – he will not be available,” Klopp told his pre-match media conference.
“He had problems with a muscle when he shot the penalty, so I think he is not available. We have to wait, but I don’t think so.”
Sakho was forced off in the first half of the Wembley showpiece after an aerial collision with his own team-mate, Emre Can.
And Klopp admitted that he is unsure over the severity of the France international’s problem.
Klopp added: “With Mama, I don’t know exactly. We had to make a decision in the moment on the sidelines.
“I think it was the right decision but until now I have heard nothing about the real issue, so I have to wait for the final judgement of the Doc.”
Liverpool drew 1-1 with City after 90 minutes after Philippe Coutinho cancelled out Fernandinho’s opener.
The Reds were 4-1 winners against Manuel Pellegrini’s side in the Premier League earlier this season.
Liverpool are nine points behind fourth-placed City in the race to secure a top-four finish.
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