Reds boss Kenny Dalglish is desperate to bring in a new left-sided defender after being forced to play Glen Johnson out of position at times last season.
After seeing his top target Gael Clichy join Manchester City, he is now looking at a number of alternatives.
Reports in France suggest one of them is Lyon's Cissokho and that a bid is imminent.
Lyon coach Remi Garde told L'Equipe that Liverpool have not yet made an offer for the 23-year-old, but he was prepared to consider any approaches.
'Aly is an important player for us, but if an offer matches our expectation, he is likely to go,' said Garde.
The French club is known to be short of cash and it is thought they are prepared to accept a bid of just £8 million, despite paying £13 million to sign Cissokho from Porto in 2009.
Liverpool are also believed to be interested in Newcastle United left back Jose Enrique, but face competition from Arsenal for the Spaniard's signature.