  In this paper we analyze the exclusive photoproduction of the $D$-meson pairs
with large invariant mass. We perform evaluations in the collinear
factorization framework and in the leading order of the strong coupling
$\alpha_{s}$, expressing the cross-section in terms of generalized parton
distributions (GPDs) of different parton flavors in the proton. We focus on the
photoproduction of the pseudoscalar-vector pairs, like e.g. $D^{\pm}D^{*\mp}$,
$D^{0}\overline{D}^{*0}$, $D_{s}^{+}D_{s}^{*-}$, which gets the dominant
contribution from the chiral even GPDs of the target, and estimate the
cross-section in the kinematics of the future Electron Ion Collider (EIC). In
all channels the amplitude of the process obtains comparable contributions from
gluons and only one of the light quark flavors. This finding signals that the
process potentially could be used to single out the contributions of the
individual chiral even GPDs of light flavors. We found that the process is
mostly sensitive to the behavior of GPDs in the so-called
Efremov-Radyushkin-Brodsky-Lepage (ERBL) region. Numerically, the cross-section
of the process is sufficiently large for experimental studies and thus can be
used as a complementary probe for studies of the partons GPDs.
