Sky Sports revealed earlier this week that free agent Zaliukas had linked up with QPR for training so that Redknapp could cast an eye over him.
Redknapp is in the market for a new centre-back as he seeks cover for Richard Dunne and Clint Hill and he admits he could offer Lithuanian Zaliukas a deal at Loftus Road if he impresses in training.
"He's been training, he's done well here," Redknapp said.
"He played in Scotland for a few years. He did well up there and we checked him out with some contacts that we've got up there and all the reports are good.
"The two areas of the team we are short in is striker and centre of defence.
"We've got two fit centre backs [Richard Dunne and Clint Hill] who are both in their thirties and we just have to hope that they stay fit.
"But playing Saturday and midweek up to Christmas is a long way to go, so if we need a bit of cover he's someone we've been looking at and it's a possibility."