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We examine various scenarios that involve a light ${\cal O}(1 TeV)$leptoquark state and select those which are compatible with the currentexperimental values for $\mathcal{B}(B_s\to \mu\mu)$, $\mathcal{B}(B\toK\mu\mu)_{\mathrm{large}-q^2}$, $R_K=\mathcal{B^\prime}(B\toK\mu\mu)/\mathcal{B^\prime}(B\to Kee)$, and which lead to predictionsconsistent with other experimental data. We show that two such scenarios arephenomenologically plausible, namely the one with a doublet of scalarleptoquarks of hypercharge $1/6$, and the one with a triplet of vectorleptoquarks of hypercharge $2/3$. We also argue that a model with a singletscalar leptoquark of hypercharge $1/3$ is not viable. Using the presentexperimental data as constraints, it is shown that the exclusive lepton flavorviolating decays, $\mathcal{B}(B_s\to \mu\tau)$, $\mathcal{B}(B\to K \mu\tau)$and $\mathcal{B}(B\to K^\ast \mu\tau)$, can be as large as$\mathcal{O}(10^{-5})$.

Palatable Leptoquark Scenarios for Lepton Flavor Violation in Exclusive $b\to s\ell_1\ell_2$ modes