  Hadron femtoscopy has turned into a powerful tool for accessing space-time
information of heavy-ion collisions as well as for studying final-state
interactions of hadrons. Recently, heavy-flavor femtoscopy has become feasible
using the ALICE detector at the LHC. We compute the correlation function of $D$
mesons and light mesons using an off-shell $T$-matrix approach to access the
two-meson wave function, and predict the correlation functions involving
charged $D^+, D^{*+},D_s^+$ and $D_s^{*+}$ with $\pi^\pm$ and $K^\pm$. From the
obtained results -- all of them accessible in $p+p$ collision experiments -- we
point up the case of $D^+ \pi^-$, which is sensitive to the lower state of the
two-pole $D_0^* (2300)$ system. The presence of such poles imprints a depletion
on the correlation function, which could potentially be detected in
experiments. While preliminary ALICE data do not show evidence of this effect,
we suggest to look into the $D_s^+ K^-$ system to explore the higher pole of
the $D_0^* (2300)$, as the depletion in the correlation function is more
pronounced. Using heavy-quark spin symmetry we also propose exploring the
effect of the two poles of the $D_1(2430)$ and predict similar structures in
the correlation functions of the $D^{*+} \pi^-$ and $D_s^{*+} K^-$ pairs.
