  This white paper explores the detectability of intermediate-mass black holes
(IMBHs) wandering in the Milky Way (MW) and massive local galaxies, with a
particular emphasis on the role of AXIS. IMBHs, ranging within $10^{3-6} \,
M_\odot$, are commonly found at the centers of dwarf galaxies and may exist,
yet undiscovered, in the MW. By using model spectra for advection-dominated
accretion flows (ADAFs), we calculated the expected fluxes emitted by a
population of wandering IMBHs with a mass of $10^5 \, M_\odot$ in various MW
environments and extrapolated our results to massive local galaxies. Around
$40\%$ of the potential population of wandering IMBHs in the MW can be detected
in an AXIS deep field. We proposed criteria to aid in selecting IMBH candidates
using already available optical surveys. We also showed that IMBHs wandering in
$>200$ galaxies within $10$ Mpc can be easily detected with AXIS when passing
within dense galactic environments (e.g., molecular clouds and cold neutral
medium). In summary, we highlighted the potential X-ray detectability of
wandering IMBHs in local galaxies and provided insights for guiding future
surveys. Detecting wandering IMBHs is crucial for understanding their
demographics, evolution, and the merging history of galaxies.
