The Reds had agreed to an 8 million-pound deal with Queens Park Rangers for the France international, but problems detected during medical tests have derailed the move.
Remy, 27, had joined up with the Reds in Boston on their preseason tour of the United States after the two clubs agreed to an 8 million-pound deal.
Remy's move from Nice to Marseille in 2010 was held up due to heart complaints, but he was later cleared to play top-level football following second tests carried out by specialists.
He joined QPR seemingly without issue three years later, and spent last season on loan with Newcastle United.
The France international had been attracting interest from Tottenham and Arsenal earlier in the summer, but Spurs pulled out of the race shortly before a fee was agreed to with Liverpool despite having held talks with the player's camp.
Remy had always favored a move to the Gunners, but he was not one of the Londoners' priority targets.
Liverpool had been interested in Swansea striker Wilfried Bony earlier this summer, but had been put off by his nearly 20 million-pound pricetag.