There was discussion in a couple places, but nothing very serious. I'll touch on one example briefly here, but should note that it falls within the 20 year rule so I don't want to get too in depth (there also isn't much to discuss).

When Georgia regained independence in 1991, there was talk about bringing back the royal family. The idea also had some support from the Georgian Orthodox Patriarch Ilia II, who called for the royal family to be re-established (while there is a separation of church and state in Georgia, the Georgian Orthodox Church is recognized for its "outstanding role" in the history of the country, and the words of the Patriarch carry a lot of authority).

There had been a Georgian kingdom (two actually, west and east), but they were ended in 1801 when the Russians annexed the country. Even so the royal family, the Bagrationis, still existed, but by this point they had split into a couple branches, and there was some dispute on who was the proper heirs to the throne: the Gruzinsky family (the name just means "Georgian" in Russian) or the Mukhrani family. This was resolved in 2009 when Ana Bagration-Gruzinsky married David Bagration-Mukhrani; the two were the respective heirs for each family, and when they had a son, Giorgi, in 2011, the families were united for the first time in centuries, and calls for the restoration of the monarchy intensified. However this was never seriously considered, and Ana and David divorced in 2013. There's been further controversy among the families since then, but that's not worth getting into except to say that the idea is effectively dead.

I'll also quickly touch on Russia here, and note that they also have a dispute over who is the rightful heir to the Romanovs. There are at least two branches claiming this, both which have tenuous claims to begin with (they both stem back to younger brothers of tsars from the 19th century, and I believe go through female descent, which was forbidden by the Pauline Laws). While the idea was never really considered after the fall of the USSR, I'm sure the confusion of who to name made it an even easier call.