  We investigate the exclusive semileptonic decays $J/\psi \to D_{(s)}^{(*)-}
{\ell}^+ \nu_{\ell}$, where $\ell=e,\mu$, within the Standard Model. The
relevant transition form factors are calculated in the framework of a
relativistic constituent quark model with built-in infrared confinement. Our
calculations predict the branching fractions $\mathcal{B}(J/\psi \to
D_{(s)}^{(*)-} {\ell}^+ \nu_{\ell})$ to be of the order of $10^{-10}$ for
$D_s^{(*)-}$ and $10^{-11}$ for $D^{(*)-}$. Most of our numerical results are
consistent with other theoretical studies. However, some branching fractions
are larger than those calculated in QCD sum rules approaches but smaller than
those obtained in the covariant light-front quark model by a factor of about
$2-3$.
