I doubt that there are reliable statistics on that point but I suspect that Armenia and Azerbaijan, smaller former Soviet republics with a highly-disproportionate share of FIDE titled players, are most likely the leaders.
Well, there is a bit old topic here, so situation might have changed a bit:
https://www.chess.com/forum/view/general/gm-s-per-capita-worldwide-1-iceland2
Realistically it is probably Armenia if you account smaller population because Armenia has around 3 million people compared to 9 million people in Azerbaijan and more GMs. But that is only if you account for the number of GMs. Countries of the former Yugoslavia are pretty high on the list as well, because of a relatively high numbers of GMs and titled players in general compared to their small populations.
There is a newer information here:
https://www.chess.com/article/view/countries-with-the-most-chess-grandmasters
There is a link to a spreadsheet on the bottom but only by total GMs.
I doubt that there are reliable statistics on that point but I suspect that Armenia and Azerbaijan, smaller former Soviet republics with a highly-disproportionate share of FIDE titled players, are most likely the leaders.