The former Hearts captain has failed to accept a contract offered to him by Craig Mather, the Ibrox side's chief executive, following a trial at Murray Park more than two weeks ago.
"Sadly, that deal has gone dead at the moment," McCoist revealed. "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 also confirmed that the protracted talks with Bosnia-Herzegovina internationalist Boris Pandza have come to an end.