  In this computational study, we explore a viable route to access the
Kitaev-Quantum Spin Liquid (QSL) state in recently synthesized monolayer of a
so-called spin-orbit assisted Mott insulator OsCl$_3$. In addition to other
magnetic ground states in different regions, the small $J_\text{H}$/$U$ region
of our Hubbard $U$--Hund's $J_\text{H}$ quantum phase diagram, obtained by
combining second-order perturbation and pseudo-Fermion renormalization group
calculations, hosts Kitaev-QSL phase. Only Kitaev interaction of a smaller
magnitude is obtained in this region. Negligibly small farther neighbor
interactions appear as a distinct feature of monolayer \os, suggesting this
material to be a better candidate for the exploration of possible Kitaev-QSL
state than earlier proposed materials. Insights from our study might be useful
to probe magnetic phase transitions by purportedly manipulating $U$ and
$J_\text{H}$ with epitaxial strain in advanced crystal growth techniques.
