The versatile left sided Cissokho, who can play as left back and can also operate in midfield, is a wanted man by both clubs, but he is believed to prefer a switch to the Merseyside outfit.
Lyon president Jean Michel Aulas has admitted that the club will look for 'some solutions' for the player who failed a medical at Milan in 2009 because of a problem with his teeth.
Lyon are struggling to compete with rivals PSG this season after the Parisan club attainted Qatar investment and need to balance the books to help clear debts and offloading Cissokho would help.
Damien Comolli will look to use his good connections with Lyon to secure a bargain signing thought to be around £6million for the 24-year-old.
Source: DSG