In the light of the question whether most early-type dwarf (dE) galaxies in clusters formed through infall and transformation of late-type progenitors, we search for an imprint of such an infall history in the oldest, most centrally concentrated dE subclass of the Virgo cluster: the nucleated dEs that show no signatures of disks or central residual star formation. We select dEs in a (projected) region around the central elliptical galaxies, and subdivide them by their line-of-sight velocity into fast-moving and slow-moving ones. These subsamples turn out to have significantly different shapes: while the fast dEs are relatively flat objects, the slow dEs are nearly round. Likewise, when subdividing the central dEs by their projected axial ratio into flat and round ones, their distributions of line-of-sight velocities differ significantly: the flat dEs have a broad, possibly two-peaked distribution, whereas the round dEs show a narrow single peak. We conclude that the round dEs probably are on circularized orbits, while the flat dEs are still on more eccentric or radial orbits typical for an infalling population. In this picture, the round dEs would have resided in the cluster already for a long time, or would even be a cluster-born species, explaining their nearly circular orbits. They would thus be the first generation of Virgo cluster dEs. Their shape could be caused by dynamical heating through repeated tidal interactions. Further investigations through stellar population measurements and studies of simulated galaxy clusters would be desirable to obtain definite conclusions on their origin.