  Current observations allow Primordial Black Holes (PBHs) in asteroid mass
range $10^{17}-10^{22}$ g to constitute the entire dark matter (DM) energy
density (barring a small mass range constrained by 21 cm observations). In this
work, we explore the possibility of probing PBH with masses
$10^{17}-10^{19}\,{\rm g}$ via upcoming X and Gamma Imaging Spectrometer (XGIS)
telescope array on-board the Transient High-Energy Sky and Early Universe
Surveyor (THESEUS) mission. While our projected limits are comparable with
those proposed in the literature for $10^{16}\,{\rm
g}\,<\,M_{\mathrm{PBH}}\,<\,10^{17}\,{\rm g}$, we show that the XGIS-THESEUS
mission can potentially provide the strongest bound for $10^{17}
\mathrm{~g}<M_{\mathrm{PBH}} \lesssim 3\times 10^{18} \mathrm{~g}$ for
non-rotating PBHs. The bounds become more stringent by nearly an order of
magnitude for maximally rotating PBHs in the mass range $5\times10^{15}\,{\rm
g}\,<\,M_{\rm PBH}\,\lesssim\,10^{19}\,{\rm g}$.
