Remy, 27, flew out to join Liverpool on their pre-season tour of the United States last Monday after QPR reportedly agreed to sell him for a fee of around £8 million ($13.6 million, 10.1 million euros).
The France international, who spent last season on loan at Newcastle United, was also thought to have agreed personal terms.
But several British media outlets, including the BBC, claimed on Sunday that Liverpool had pulled out of the transfer due to worries about Remy’s physical condition.
Remy, who began his career at Lyon, joined QPR from Marseille in January 2013 for a club-record fee of around £8 million.
Following QPR’s relegation to the Championship at the end of his first season, he spent the 2013-14 campaign on loan at Newcastle, scoring 14 goals in 26 Premier League games.
QPR will play in the Premier League again next season after securing promotion via the play-offs in May.
Remy has scored five goals in 25 international appearances for France and was a member of the squad that reached the quarter-finals at the World Cup.
Liverpool have already spent in the region of £60 million during the close-season transfer window.
They have signed England pair Adam Lallana and Rickie Lambert from Southampton, German midfielder Emre Can from Bayer Leverkusen, and Serbian forward Lazar Markovic from Benfica.
Lallana, however, will miss the start of the season after being ruled out for up to six weeks with a knee injury.
Liverpool are also reported to be close to completing a £20 million move for another Southampton player, Croatian centre-back Dejan Lovren.
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