Boss Ally McCoist expects to find out in the next couple of days if Marius Zaliukas will become Rangers' latest recruit.
The former Hearts skipper was offered a deal earlier this week and has returned to his native Lithuania to consider the offer.
Zaliukas - who left the Jambos in the summer - impressed the manager while training with the Light Blues and McCoist should know in the next 48 hours or so whether or not he has landed the defender.
He said: "Marius has gone back home.
"We have put an offer to him and we would be very hopeful of speaking to him in the next couple of days to see whether or not he will take that offer up."
If the answer is no, McCoist says he has other options to bolster his defence, with talks still ongoing with Bosnian international Boris Pandza.
He added: "I know we are still in negotiations and speaking to Boris Pandza's agent.
"I know Craig (Mather, chief executive) has been speaking to him.
"I will speak to Craig later today to see if there are any further developments. We are still pursuing a couple of lines in central defence."
Asked if there was a chance of signing both players, McCoist said: "I don't know. I couldn't say it would be both or one or the other.
"I would have to wait and see what progress has been made in terms of the details of the offers."
Greek defender Anestis Argyriou is the latest player to head for the Ibrox exit door and McCoist says more could follow.
He said: "There possibly could be. I think that's another four boys who have left the club in the last month or so.
"I couldn't give you specific names but, like most clubs, there will be activity and players hopefully coming in as well as leaving."
Meanwhile, McCoist declined to be drawn on where the Ramsdens Cup final should be held this year if semi-finalists Rangers make the last two.
Competition organisers would likely seek a bigger than usual venue, given the size of the Light Blues support.
With Hampden unavailable due to the Commonwealth Games, Celtic Park and even Ibrox itself could be possible alternatives.
McCoist said: "I would be far happier having this conversation if we are in the final. I'll probably save it for then.
"At this moment in time, it's for the powers that be to discuss where the final will be.
"I'll certainly give you my tuppence-worth if we are fortunate enough to beat Stenhousemuir away.
"To be honest, if you were asking most of the players, they would want to play in a bigger stadium with a full house.
"In terms of the sponsors, I would imagine they would want to make it as big an occasion as possible. These are factors that would have to come into it as well."
Why are you making commenting on The Herald only available to subscribers?
It should have been a safe space for informed debate, somewhere for readers to discuss issues around the biggest stories of the day, but all too often the below the line comments on most websites have become bogged down by off-topic discussions and abuse.
heraldscotland.com is tackling this problem by allowing only subscribers to comment.
We are doing this to improve the experience for our loyal readers and we believe it will reduce the ability of trolls and troublemakers, who occasionally find their way onto our site, to abuse our journalists and readers. We also hope it will help the comments section fulfil its promise as a part of Scotland's conversation with itself.
We are lucky at The Herald. We are read by an informed, educated readership who can add their knowledge and insights to our stories.
That is invaluable.
We are making the subscriber-only change to support our valued readers, who tell us they don't want the site cluttered up with irrelevant comments, untruths and abuse.
In the past, the journalist’s job was to collect and distribute information to the audience. Technology means that readers can shape a discussion. We look forward to hearing from you on heraldscotland.com
Comments & Moderation
Readers’ comments: You are personally liable for the content of any comments you upload to this website, so please act responsibly. We do not pre-moderate or monitor readers’ comments appearing on our websites, but we do post-moderate in response to complaints we receive or otherwise when a potential problem comes to our attention. You can make a complaint by using the ‘report this post’ link . We may then apply our discretion under the user terms to amend or delete comments.
Post moderation is undertaken full-time 9am-6pm on weekdays, and on a part-time basis outwith those hours.
Read the rules hereComments are closed on this article