Remy, 27, flew to Boston last week to join up with the Liverpool squad and undergo a medical examination but the Premier League club have put a stop to the deal following the results of the examination.
Neither Liverpool nor QPR have made any official comment on the deal falling through.
Remy, who scored 14 goals in 26 Premier League appearances while on loan at Newcastle United last season, had agreed personal terms with Liverpool, but is now set to return to QPR.
Liverpool began the move after their bid of 8.5 million pounds ($14.5 million) for the player triggered a release clause for his departure from the west London club.
Remy was part of the France squad that reached the World Cup quarter-finals in Brazil, making two substitute appearances, in the 0-0 group stage draw with Ecuador and the 1-0 quarter-final defeat by Germany.
He was expected to be among a raft of new signings at Anfield as manager Brendan Rodgers bids to strengthen his squad ahead of the new season in which Liverpool return to the Champions League for the first time since 2009.
Liverpool finished second to Manchester City in the Premier League last season.
Southampton's Rickie Lambert and Adam Lallana, who will miss the first six weeks of the season with a knee ligament injury, joined Liverpool along with Emre Can of Bayer Leverkusen and Benfica's Lazar Markovic for a combined cost of 59 million pounds.
Croatian defender Dejan Lovren is also expected to arrive at Anfield in a 20 million-pound move from Southampton while Belgian teenager Divock Origi, who also made his mark at the World Cup, is thought to be arriving from Lille on a 10 million-pound deal, but could be loaned back to the French club.
Rodgers has money to spend after the 75 million ($128.2 million) sale of Uruguay striker Luis Suarez to Barcelona.