In the modern era, seven countries (Argentina, Australia, Chile, France, New Zealand, Norway, and the United Kingdom) have made official territorial claims on part of Antartica. These claims are not widely recognized and the Antarctic treaty, which is widely ratified, forbids new claims.
While the US and Russia have ratified the treaty, they have also reserved the right to make a territorial claim. And beside, treaties can be exited or disregarded.
Fine print:
Official claim, by the country governeming body
Can be a new claim from one of the country that already has a claim, including an expansion of that claim, or a new claim for a previously uninvolved country, But not just re-stating a pre-existing claim.
Note that there is no protection against "spam claim" (official but unserious claim for attention or other motive from a country, for instance, from a nation that cannot credibly defend their claim militarily), so bet with that in mind
Antarctica "mainland", not islands or oceanic shelves (by themselves, could be part of the claim)
Territorial claim, including claiming sovereignty. Only granting oneself free mining right, or disregarding other countries claim does not constitute making a claim for the country.
No unofficial claims (like Brazil) nor historical claims
Reserve right to N/A on ambiguity after discussion in the comments
Related markets for specific country possible claims:
https://manifold.markets/CamillePerrin/will-russia-make-a-territorial-clai
https://manifold.markets/CamillePerrin/will-the-usa-make-a-territorial-cla