  We discuss the single diffractive production of $c \bar c$ pairs and charmed
mesons at the LHC. For a first time we propose a $k_t$-factorization approach
to the diffractive processes. The transverse momentum dependent diffractive
parton distributions are obtained from standard (collinear) diffractive parton
distributions used in the literature. In this calculation the transverse
momentum of the pomeron is neglected with respect to transverse momentum of
partons entering the hard process. We also perform the first evaluation of the
cross sections at the LHC using the diffractive transverse momentum dependent
parton distributions. The results of the new approach are compared with those
of the standard collinear one. Significantly larger cross sections are obtained
in the $k_t$-factorization approach where some part of higher-order effects is
effectively included. The differences between corresponding differential
distributions are discussed. Finally, we present a feasibility study of the
process at the LHC using proton tagging technique. The analysis suggests that
the measurement of single diffractive charm production is possible using ATLAS
and CMS/TOTEM detectors.
