Keita picked up an injury to his hip prior to Liverpool’s UEFA Super Cup victory over Chelsea last week.
Klopp previously revealed the club were unsure about the seriousness of Keita’s injury.
“[He is] not available,” he said ahead of the 2-1 win at Southampton at the weekend.
“It’s a muscle thing and we don’t know exactly how long it will take. But he’s not available.”
But now the Mirror reports that Keita will miss the game with Arsenal on Saturday and could be out for a while.
Liverpool have had a strong start to the season, winning both of their Premier League matches.
Their win over Southampton came after a 4-1 victory over newly-promoted Norwich.
Sadio Mane, Roberto Firmino and Mohamed Salah have all found the net already this season.
But Klopp has revealed there’ll be some rotation to his side this season.
“No football player should play 50 or 60 games a season, especially not in these intense positions,” he said.
“Goalie and a centre-half maybe do it but all the rest, give whatever you have and next game maybe somebody else will do the job.
“That’s the plan, but we can only do that if they all stay fit.
”A lot of times in my life I had sensational players always [but] not world-class players.
“Now, thank God I have them and they make the difference. We don’t have to talk about that.
“Sadio Mane, Bobby Firmino, Mo Salah – these guys in the last situation are really outstanding.
“They were a constant threat, however tired they are. That’s brilliant and, of course, made the difference. We don’t have to talk about that.”
Liverpool host Arsenal on Saturday at 5.30pm.