Redknapp, who was speaking after his side's victory at West Bromwich in the FA Cup third-round replay, told BBC Radio 5Live: "Loic Remy has had a medical and I think that's all sorted now.
"Loic Remy is a good player, Newcastle do very well in the French market as well, and I looked at him an awful lot while I was at Spurs, but they wanted £20m for him.
"Yann M'Vila was the same. They turned down £28m for him 18 months ago so if we can pull off this it will be fantastic."
Rangers' late win tonight saw them set up a fourth-round meeting with West Ham or Manchester United.