  We examine various scenarios that involve a light ${\cal O}(1 TeV)$
leptoquark state and select those which are compatible with the current
experimental values for $\mathcal{B}(B_s\to \mu\mu)$, $\mathcal{B}(B\to
K\mu\mu)_{\mathrm{large}-q^2}$, $R_K=\mathcal{B^\prime}(B\to
K\mu\mu)/\mathcal{B^\prime}(B\to Kee)$, and which lead to predictions
consistent with other experimental data. We show that two such scenarios are
phenomenologically plausible, namely the one with a doublet of scalar
leptoquarks of hypercharge $1/6$, and the one with a triplet of vector
leptoquarks of hypercharge $2/3$. We also argue that a model with a singlet
scalar leptoquark of hypercharge $1/3$ is not viable. Using the present
experimental data as constraints, it is shown that the exclusive lepton flavor
violating 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
$\mathcal{O}(10^{-5})$.
