The former Hearts captain has failed to accept a contract offered to him by chief executive Craig Mather following a trial at Murray Park more than two weeks ago.
McCoist told RangersTV: "Sadly, that deal has gone dead at the moment and I think Marius has one or two other options.
"Craig effectively put an offer to him which wasn't met so we're just about closing that one off at this moment in time."
Rangers had also been in protracted talks with Bosnia-Herzegovina international Boris Pandza but they have confirmed those discussions ended. Pandza last week accused the club of being unprofessional for failing to come up with a concrete offer.
McCoist, who has been lining up with a central defence of Lee McCulloch and Bilel Mohsni, added: "It looks like we'll have to go with what we've got and, to be fair, we've been reasonably solid defensively.
"Hopefully we'll just carry a little bit of luck with injuries and suspensions and we'll see where that takes us.
"We've got options in guys like Sebastien (Faure) and Emilson (Cribari). Big Jig (McCulloch) has been playing at the back with Bilel but there are others too."
Two other centre-backs, Chris Hegarty and Ross Perry, are working back to fitness following ankle surgery.
Meanwhile, McCoist is not anticipating any backlash against Ian Black if the midfielder returns from his three-match ban for breaching gambling rules when Rangers host Stenhousemuir on Saturday.
The former Hearts midfielder admitted betting on his own team not to win on three occasions in recent years, one of which was when he bet on Rangers to draw with East Stirlingshire on his coupon. Rangers beat Shire 4-2 with Black scoring their third goal.
McCoist said: "I don't foresee any problems with Ian coming back in, I genuinely don't. I think he's got a very good rapport with the Rangers support and I'd be very hopeful that will continue.
"We think what he did was daft but we don't think it was sinister, which is very, very important. I'm not saying it was right because it wasn't.
"I'll never tell the fans what to do in terms of who their favourites will be but I'd be very hopeful they'll see things in the same way we've seen it. It was daft, nothing more than that.
"Ian will certainly come back into the reckoning at the weekend, that's for sure."
- Sports & Recreation
- Craig Mather
- Bilel Mohsni