France international Remy was widely expected to complete an £8.5 million move to Anfield this week as the Merseyside club continue the process of trying to replace Luis Suarez.
However, Liverpool pulled the plug on the deal on Sunday, with manager Brendan Rodgers remaining vague as to the reasons behind that decision after his side's friendly win over Olympiacos.
It is widely believed that Liverpool detected a problem during Remy's medical, with Rodgers saying only that the issue has "happened before".
But QPR boss Redknapp refuses to believe the switch fell through due to any physical issues, and has challenged the 27-year-old striker - who spent last season on loan at Newcastle - to fire his team to top-flight safety following their promotion from the Championship.
"He'll come back here," Redknapp confirmed at a media conference to introduce QPR's new signing Rio Ferdinand.
"I just can't believe it. I only know what I've seen and heard - I don't see how he failed a medical, he had a stringent medical here, one at Marseille, one at Newcastle, one at France.
"It's not possible, you couldn't find a fitter lad than he is, there must be another reason. They must have changed their mind or gone in a different direction.
"It's disappointing for him, (but) from the club's point of view we've got a great striker. He's a good lad, good player [and a] good professional.
"Their loss is our gain. He's a striker capable of 20 goals in the Premier League, [and] that's we need now - for him to get 20 goals for QPR in the league."
Remy scored 14 goals in 26 Premier League appearances for Newcastle last term - form that earned him a place in France's World Cup squad.
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