The striker's transfer has been cancelled following his examination, which he underwent in Boston on Tuesday.
The results took longer than usual to come through as the medical took place away from Merseyside. Neither club has commented officially, and the specific issue is not known.
A possible heart defect was revealed in 2010, when Remy joined Marseille from Nice, but the transfer went through after further tests saw doctors give Remy the all-clear.
Back then, it was decided that Remy was still suitable for a career in professional football. However, it is unknown whether the latest problem is related to his cardiovascular, or another issue.
Liverpool had agreed an £8.5m deal to sign Remy from QPR after he impressed on loan at Newcastle last season, earning himself a place in France's World Cup squad.
Brendan Rodgers must look elsewhere to replace Luis Suarez, who has joined Barcelona, though Rickie Lambert arrived before the World Cup.
Liverpool are reportedly close to signing Belgian striker Divock Origi for £12.5m - they had originally planned to loan him back to Lille for the 2014/15 season but may now wish to press the 19-year-old into immediate service.