  The origin of arcmin-sized Odd Radio Circles (ORCs) found in modern all-sky
radio surveys remain uncertain, with explanations ranging from
starburst/AGN-driven shocks to supernova remnants (SNRs) in the low-density
ambient medium. Using well-calibrated radio light curve models, we assess the
possibility that ORCs are radio SNRs evolving in low ambient densities. Our
models imply that ORCs 1-5 and J0624-6948 (near the LMC) as SNRs must be within
200 kpc and 100 kpc from the Sun respectively, given their observed flux
densities and angular sizes. To be evolving in the circumgalactic medium of the
Milky Way, our models require ORCs 1-5 to be ejecta-dominated SNRs within 50
kpc, evolving in ambient densities of $(0.2-1.2) \times 10^{-3}$ cm$^{-3}$.
However, this is statistically unlikely because ORCs 1-5 would have ages $<640$
yrs, much smaller than their expected lifetimes of $\gtrsim$10$^5$ yrs at these
densities, and because the low SN rate and steep profile of the stellar halo
imply a negligible number of ORC-like SNRs within 50 kpc. The circumgalactic
medium SNR scenario for J0624-6948 is more likely (though still low
probability) compared to ORCs 1-5, as our models allow J0624-6948 to be
$\lesssim$3000 yrs. On the other hand, the interpretation of J0624-6948 as a
Sedov-Taylor SNR at 50 kpc (LMC) distance is possible for a wide range of
ambient densities ($6 \times 10^{-4} - 0.5$ cm$^{-3}$) and ages
$\sim$$(0.2-2.6) \times 10^4$ yr, while also being consistent with the local HI
environment.
