The Reds jetted out to Boston on Sunday to begin their pre-season tour and Press Association Sport understands they will be joined by the 27-year-old Frenchman late on Monday.
Remy, who scored 14 goals on loan at Newcastle last season during QPR's year out of the Premier League, will undergo his physical examination by Liverpool's medical team on Tuesday and is likely to be confirmed as their fifth summer signing - for a fee in the region of B£8million - the following day.
Belgium striker Divock Origi is expected to make the same trip as Remy for a medical with a deal virtually concluded with Lille but no date has been set for that as yet.
While Rodgers is bringing in more strikers it seems he cannot get rid of another as Fabio Borini wants to stay and fight for his place at Anfield despite the club accepting a B£14million bid from Sunderland where the Italian had a successful loan spell last season.
Borini played in Saturday's friendly win over Preston and has travelled with the squad to America.
"He wants to remain on Merseyside," his agent Marco de Marchi told Tuttomercatoweb.com.
"Sunderland have made a large offer of 18 million euro (B£14million) to sign him but Fabio wants to stay.
"His project with Liverpool started two years ago when he left Roma; he began a journey and it is a major project for him.
"He should not be judged on his first year; he was out for six months with various injuries and during the past year he took a step back by going to Sunderland and he has had an extraordinary season.
"His future? Now, after the loan, Liverpool have not told me anything. I think he will stay, he is convinced that he will play."
When asked what Borini thought about his chances being limited, De Marchi added: "(Raheem) Sterling, (Daniel) Sturridge, (Rickie) Lambert and now Remy? At Roma he was with (Francesco) Totti, (Dani) Osvaldo, (Erik) Lamela and Bojan (Krkic).
"He has no fear of playing alongside anyone and for me he can play a part within any top club."
The suggestion coming from the Croatia international's camp is that Saints, from whom Liverpool have already bought Lambert and Lallana this summer, are willing to accept the Merseysiders' B£20million offer.
However, that has not been officially communicated to Liverpool by Southampton and so negotiations are continuing.
Should a deal for Lovren be agreed it would cast further doubt on the future of Daniel Agger, who has been linked with an exit since before the end of last season.
"It is no secret that I had problems last season and I am considering things," the Denmark captain told BT, a newspaper in his homeland.
"How things turned out last season is not acceptable for me.
"Many things can happen in football and I do not want to exclude anything.
"I am here now and it is up to me to show the coach that I should play."
Agger has travelled with Liverpool and trained with the 33-man squad at their base at Harvard University, although Rodgers was absent as he is suffering with a virus.
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- Brendan Rodgers
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- Fabio Borini