We start from the assumption that the $\Lambda_c(2940)$ and $\Lambda_c(2910)$ correspond mostly to $D^\ast N$ bound states with $J^P = 1/2^-$ and $3/2^-$, respectively. Then, adding a $D$ meson as a third particle, and assuming that the $DN$ and $DD^\ast$ interactions are mainly dominated by the $\Lambda_c(2765)$ and $T_{cc}(3875)$ resonances, we look for the possible binding of the $D^\ast DN$ three body system within the framework of the Fixed Center Approximation. We find one state for each spin channel with a binding of about $60$ MeV with respect to the $\Lambda_c(2940) D$ and $\Lambda_c(2910) D$ thresholds and a width of about $90$ MeV. As an alternative picture we also study the system as a cluster of $DN$ and a $D^\ast$ meson interacting on the cluster, and find similar results. The observation of these $J^P = 1/2^+,\, 3/2^+$ states would provide new and valuable information concerning the $DN$ and $D^\ast N$ interaction, a topic of current interest.