And Sky sources report that the £8.5m deal to sign Remy from Queens Park Rangers should be finalised by Thursday.
The 27-year-old caught the eye at QPR towards the end of the 2012/13 season but was unable to keep the London side in the top flight and spent last season on loan at Newcastle United.
He impressed in the north-east, scoring 14 goals in 26 Premier League appearances, and made it into the France squad for the World Cup in Brazil, where he came off the bench on a couple of occasions.
Remy is believed to have a release clause in his QPR contract which allows him to join clubs who have qualified for the Champions League for a fee of £8.5m.
And the former Marseille man is now said to have joined Liverpool on their pre-season tour of America.
However, Reds boss Brendan Rodgers told the media in Boston that he was not willing to comment on possible transfer moves.
"I shall not talk about speculation on any player until they have signed," he said.
"I will talk about them when they are signed and have agreed to come in."