The 29-year-old free agent linked up with QPR for training earlier this week so that Redknapp could assess his credentials.
"He's been training and he's done well here," Redknapp told reporters. "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 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."
Zaliukas made 192 SPL appearances during seven seasons at Tynecastle between August 2006 and May 2013.