Southampton defender Virgil van Dijk has also been targeted by Liverpool, but they were forced to withdraw their interest and publicly apologise to their fellow Premier League club after being accused of tapping up.
When asked about the Reds' Keita pursuit during a press conference in Hong Kong, Klopp told reporters: "There's nothing new to say about this. It's the transfer market. Everything is open until August 31.
"I am not easy to frustrate. It's the transfer market. Sometimes things work out, sometimes they don't. That's how it is. I'm still relaxed."
Liverpool's first game of the season will be away to Watford on August 12.