Manager Brendan Rodgers has confirmed the club are looking to add cover at left back, with Jose Enrique and youngster Jack Robinson the only current options at the club.
The Reds would pay an initial loan fee of round £850,000, with the option to buy the player on a permanent deal for £3.5million next summer.
The 25-year-old joined Valencia in a £7million deal from Lyon, but the Spanish club are having to cut costs after failure to qualify for the Champions League last season.
The Reds are hoping a good negotiation with the Spaniards would put them in pole position to sign striker Roberto Soldado, who Rodgers has earmarked as a potential replacement for Luis Suarez.
Frenchman Cissokho is also attracting interest from Sunderland but would favour a move to Anfield.
Meanwhile Italian giants Lazio are reportedly keen to sign Liverpool forward Fabio Borini.
The Italian striker only joined the club last summer from Roma for a fee of over £10million, but endured a miserable debut season at the club, which saw him pick up two serious injuries and manage just two goals in all competitions, including just one Premier League strike.
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