Sky Sports reported on Saturday that the two Premier League clubs had agreed an £8.5million fee for Remy's transfer to Anfield, and it is now understood that fee could rise to £11m.
The Reds flew out to the US for their pre-season tour on Sunday, where they face Italian side Roma at Fenway Park as their first fixture of the Guinness International Cup, and France international striker Remy is on his way to join them.
And he could be joined by centre-back Dejan Lovren later this week following a step forward in negotiations over his transfer from Southampton.
Saints boss Ronald Koeman insists he “doesn’t want to lose” Lovren, but the clubs are believed to have agreed a fee and the Croatia international defender is keen on the move.
Remy, meanwhile, has a release clause in his contract which allows him to speak to clubs in the UEFA Champions League if a fee is agreed, and the two clubs made headway over the weekend.
He attracted the attention of a host of European clubs with an impressive season-long loan at Newcastle last season in which he scored 14 goals in 26 Premier League appearances.
QPR are keen to offload the expensive forward, with chairman Tony Fernandes recently speaking of his desire to sort the player's future out quickly.
Remy, 27, and Lovren, 25, would be the Reds' fifth and sixth signings of the current transfer window following the arrivals of Adam Lallana and Rickie Lambert from Southampton, Emre Can from Bayer Leverkusen and Lazar Markovic from Benfica.