  The proposal for a high-energy muon collider offers many opportunities in the
search for physics beyond the Standard Model (BSM). The collider by
construction is likely to be more sensitive to the muon-philic models,
primarily motivated by the BSM explanation of muon $(g-2)$ excess and quark
flavor anomalies. In this work, we explore the potential of the proposed muon
collider in the context of such models and focus on one such model that extends
the Standard Model (SM) with a leptoquark, a vector-like lepton, and a real
scalar. In this model, we propose searches for TeV scale leptoquarks in
$2\mu+2b+mET$ channel. Notably, the leptoquark can be produced singly at the
muon collider with a large cross-section. We have shown that a significant
signal in this channel can be detected at a 3~TeV muon collider even with an
integrated luminosity as low as $\sim 10$~fb$^{-1}$
