Remy joined Harry Redknapp's side in January from French club Marseille, but had a release clause implemented in the likely event that Rangers failed to beat the drop.
And with the West London club now 10 points adrift from safety with just four games to play, Liverpool are ready to snatch the £8m Frenchman before he drops down to the second tier of English football.
Arsenal manager Arsene Wenger is also keen on Remy, having scouted him during his Ligue 1 days, while Tottenham have also been linked with the 26-year-old.
But Brendan Rodgers is preparing to move swiftly to secure Remy, who has adapted to the Premier League quickly scoring five goals in 10 games.
Remy may have to lower his reported £90,000 a week wages to secure a move away from QPR, who he is currently contracted to until 2017.
Arsenal and Liverpool are also going head-to-head over Swansea defender Ashley Williams.