It was reported earlier in the week that Kenny Dalglish was considering a £6m bid for the French international, but talkSport reports that the Ligue 1 side require significantly more.
“There have been calls from England, but there is no question of letting Dimitri leave at any price,” St Etienne president Roland Romeyer said.
A Reds approach has been on the cards since director of football Damien Comolli moved to Anfield from St Etienne.
The 24-year-old, whose contract runs to 2013, scored 13 goals in his 33 appearances last season.
Meanwhile, Liverpool are also eyeing Aston Villa’s Stewart Downing and Stade Brest’s Nolan Roux to strengthen the squad.