The Valencia defender has revealed the two clubs remain at loggerheads over the deal, with the Liga side keen for a sale and the Reds hoping for a loan with an option to buy.
The Premier League side has been busy in the transfer market with four signings to date - Simon Mignolet, Kolo Toure, Iago Aspas and Luis Alberto - but the Reds are light on fullbacks following the retirement of Jamie Carragher and Jack Robinson's loan move to Blackpool.
And Cissokho has now claimed he is close to joining Liverpool, but he states the two clubs are at loggerheads over the structure of the deal, with Valencia after a sale and Liverpool keen on a loan-to-buy option.
"Liverpool have made me an offer and it is true that I have reached an agreement with them," Cissokho told Le 10 Sport. "It is now up to the clubs to agree terms. I expect to know more later this week.
"If nothing happens this week, it probably means that I will not be going to Liverpool.
"The conditions of the transfer are the problem. Liverpool prefer a loan deal with an option to buy, while Valencia want to sell straight away. If the transfer doesn't take place, it's not a problem either. I am feeling well at Valencia."
Cissokho made 20 appearances for Valencia last term after joining from Lyon on a four-year deal.