The 25-year-old left back has been linked with Sunderland as well as Liverpool, but the report claims Brendan Rodgers has won the race to sign him.
The agreement will bring Cissokho on a season-long loan for an initial fee of €1m. A further €4m to be paid at the end of the campaign would bring him to Liverpool on a permanent basis.
The Valencia full-back would offer competition for Jose Enrique. Primarily an attacking left-back, Cissohko has one cap for France and earned a move to Valencia after impressing in the Champions League with Lyon and Porto.
The report claims an agreement in principle has been reached between Liverpool and Valencia. And all that remains to be sorted is paperwork before Cissokho can join up with the rest of the Reds squad on pre-season.
He would join Luis Alberto and Iago Aspas as other Liverpool signings from La Liga, while Suso is set to go the other way - swapping Anfield for Almeria on loan next term.