Monreal has four Spain caps while Cissokho has played once for France.
Liverpool are already well advanced with deals for Sunderland's Jordan Henderson, Blackburn's Phil Jones, Connor Wickham of Ipswich and also want Blackpool's Charlie Adam.
Big summer of spending: Liverpool boss Kenny Dalglish will add several new faces
They are in talks with Roma goalkeeper Doni's agent after the clubs agreed a ?1.5m move, leaving manager Kenny Dalglish needing just a winger.
Aston Villa's Stewart Downing remains in the frame.
Straight choice: Aly Cissokho (left) and Nacho Monreal
Liverpool striker Suarez delighted with impressive start to Anfield careerDalglish set to kick-off Reds summer spree with ?1m Roma keeper DoniAll the latest Liverpool news, features and opinion
Explore more:People: Kenny Dalglish, Stewart Downing, Charlie Adam Places: Lyon, Liverpool, Spain, France