Remy was set to complete a switch to Anfield over the weekend but Liverpool called the deal off due to what are believed to be concerns over the 27-year-old's health.
The France forward encountered problems when he moved from Nice to Marseilles in 2010
The medical discovered a heart defect but further tests convinced Marseilles to complete the transfer.
"I don't really see how he could have failed a medical," Redknapp said.
"He had a stringent medical here - one at Marseilles, at Newcastle and with the French team at the World Cup.
"He's never had a problem with his fitness - you couldn't meet a fitter lad.
"I've seen the story break but I don't know how there can be an issue with his fitness - he's got no problems whatsoever."
Remy spent last season on loan at Newcastle where he scored 14 goals for the Magpies in the Barclays Premier League.
The striker was out for almost a month with a calf problem towards the end of the campaign but Redknapp believes there must be another reason for Liverpool pulling the plug.
"There must have been a breakdown or they've changed their mind or they've decided to move in another direction," Redknapp said.
"It's not fair on him because it's my opinion and the opinion of everybody else - he's never had a problem before."
Remy has also attracted interest from Tottenham and Arsenal in the past but Redknapp would be delighted if the striker remained at Loftus Road.
"From our point of view we've got a fantastic striker - one of the best strikers in the Premier League in my opinion," Redknapp said.
"Liverpool's loss is our gain
When he went to Newcastle last year I said he was capable of 20 goals in the Premier League so that's what we need him to do.
"I'm disappointed for the boy that his move didn't happen but from a selfish point of view, I've got a great striker back here now.
"If he's here, we'll be delighted to have him - he's a good lad, a good player and a good professional."
Source : PA
Source: PA