Bosnia international Pandza has been in talks with the club for a number of weeks, while former Hearts skipper Zaliukas has been training at Murray Park since last Thursday.
McCoist has already recruited eight new signings for Rangers' assault on Scottish League One this season.
But he may be restricted to adding just one central defender after being unable to offer trialist midfielder Sam Kelly a deal.
McCoist told the club's website: "I've made it clear we'd love to bring in a centre-half and Marius has done really, really well.
"He says he hasn't done an awful lot lately but you wouldn't know it to look at him because he is certainly in good shape.
"Marius has come in to train with us and is a very fit lad.
"Himself and Boris are two players we've been looking at and I'm very keen to strengthen that department.
"I'm not sure if there's a budget for both and I would need to speak to Craig [Mather, chief executive] about that.
"He's very aware of our concerns about getting another centre-back in.
"We couldn't afford to offer Sam a deal so that would possibly indicate we'd be looking at getting one centre-half in."
The Light Blues boss also confirmed that Scott Gallacher and Andy Mitchell could both secure loan moves later this week.
Goalkeeper Gallacher looks set for a temporary switch to fellow League One side Airdrieonians, which would allow McCoist to sign veteran keeper Steve Simonsen, while Mitchell has had interest from both Arbroath and Annan.
McCoist said: "I've spoken to Jimmy Boyle at Airdrie and I know Scott spoke to him on Friday as well about going there.
"Hopefully we're going to get something over the line there in the next couple of days, where Scott can still train here and continue his work with Jim Stewart and Jim Henry.
"At the same time, he'll train with Airdrie when they meet and obviously play with them as well.
"That way, we feel we'd be getting the best of both worlds. It ticks all the boxes.
"Andy has an opportunity to go out on loan as well and I know there are one or two clubs who are interested.
"Annan have been keen and I know Arbroath were too. I would encourage it because we need all our players to be playing, especially our younger ones."