The QPR man looks set to move on from Loftus Road in the coming weeks after returning from a season-long loan stint at Newcastle.
Arsenal were thought to be leading the race along with Spurs, but both sides have pulled out.
The Gunners are said to have baulked at Remy’s £80,000-per-week wage demands, while the Lilywhites are not ready to go all out to persuade the player to look at a club without Champions League football – which is thought to be the forward’s big wish.
Liverpool have emerged as late comers in the tussle, and now they look on course to nab the 27-year-old after holding talks with his advisors.
The Reds are fresh from selling Luis Suarez to Barcelona for £70m, and could be more than willing to trigger the Les Bleus World Cup star’s £8m release clause.
However, they want him to dip his salary expectations, as he would be a back-up man for Daniel Sturridge.