The Anfield side were believed to be keen on signing the 23-year-old left-back, capped once by France, to fill the void on the left side of their back four.
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But Bernard Lacombe, an advisor to OL president Jean-Michel Aulas, has said that the Premier League club will need to make contact if they are genuinely interested in the player.
"If Liverpool is attracted in Cissokho, they have to come to us," he told L'Equipe.
Cissokho, who arrived at Lyon from Porto in the summer of 2009, has long been linked with a move to England, with Arsenal and Manchester City both said to have previously been monitoring the defender.
When asked about the possibility of a move to England earlier this year, Cissokho expressed a willingness to consider a move to the Premier League.
"I think this is a league that suits me. It is a league where you can show power and get forward.
"Whether it is clubs like Manchester United, Arsenal, Man City, now Liverpool or Chelsea, they are clubs you dream about."
