We point out an interesting theoretical prediction for elliptical galaxies residing inside galaxy clusters in the framework of modified Newtonian dynamics (MOND), that could be used to test this paradigm. Apart from the central brightest cluster galaxy, other galaxies close enough to the centre experience a strong gravitational influence from the other galaxies of the cluster. This influence manifests itself only as tides in standard Newtonian gravity, meaning that the systematic acceleration of the centre of mass of the galaxy has no consequence. However, in the context of MOND, a consequence of the breaking of the strong equivalence principle is that the systematic acceleration changes the own self-gravity of the galaxy. We show here that, in this framework, initially axisymmetric elliptical galaxies become lopsided along the external field's direction, and that the centroid of the galaxy, defined by the outer density contours, is shifted by a few hundreds parsecs with respect to the densest point.