The Lithuanian international has been without a club since he left Tynecastle at the end of last season after seven years in Edinburgh.
Now 29, the defender played 220 times for the Jambos following his move from FBK Kaunas in 2006 and scored 14 goals.
Manager McCoist has spoken frequently in recent times about his desire to recruit another centre-back and a striker to add to his eight summer signings so far.
Discussions have been taking place of a number of weeks about the possibility of Bosnian stopper Boris Pandza moving to Ibrox.
No agreement has been struck there as yet though and Zaliukas is the player currently being assessed by the Ibrox boss.
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