The Reds have been heavily linked with a bid to bring the 22-year-old midfielder to Anfield this summer but there is yet to be any official announcement from the Merseyside outfit.
It remains to be seen whether the Reds will be able to convince RB Leipzig to sell the Guinea international this summer.
Liverpool were publicly linked with a bid to land Virgil van Dijk from Southampton last month but a move failed to materialise after the Reds were alleged to have made an illegal approach to sign the player by Southampton.
And Clarke reckons that Keita move could well end up fizzling out like the proposed Van Dijk deal.
Clarke is quoted as saying by the Daily Express: “This is an ongoing saga.
“Are they going to stump up enough money to sign Naby Keita from Leipzig? Are they or not?
“I think they went with £60m, £62m, it’s like they’re bidding for a house and are going up in very small increments.
“If they really want him, surely just get it done.
“It’s so public and that’s the issue with Van Dijk, the Keita chase, it’s all very, very public.
“I can see this one fizzling out.”
Liverpool have already signed two players this summer but will be keen to add further reinforcements as they prepare for Jurgen Klopp’s second season in charge at the club.
The Reds are gearing up for a return to the Champions League next term after their fourth-placed finish last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news