The Reds had agreed a €10 million deal with Queens Park Rangers for the France international, but problems detected during medical tests have scuppered the move
Remy, 27, had joined up with the Reds in Boston on their pre-season tour of the United States after the two clubs agreed a €10 million deal.
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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 with Liverpool despite having held talks with the player's camp.
Remy had always favoured 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 near-€25m pricetag.