Free agent Ben Haim has been training with Rangers for the last few weeks after leaving Portsmouth last August.
The Israel international has impressed Redknapp during his stint at the club and he is now ready to hand the former Bolton and Chelsea defender a short-term deal until the end of the season.
"Tal has worked hard and we will look to give him a contract until the end of the season," said Redknapp. "He may be added to the squad. He is keen to have a go with us."
Redknapp has made defensive reinforcements one of his top priorities in this month's transfer window.
"We still need to strengthen up. No doubt about that," added Redknapp.
"The two centre-halves [Ryan Nelsen and Clint Hill] have done miracles. I think they're both 35 years of age."