We investigate gradient Einstein solitons admitting closed conformal vector fields. Under constant scalar curvature, we establish rigidity results showing that complete solitons with non-parallel closed conformal vector fields are isometric to Euclidean space. In the non-compact case, we prove that solitons with homothetic closed conformal vector fields are locally conformally flat in dimension four and possess a harmonic Weyl tensor in higher dimensions. Furthermore, we obtain a classification result, showing that such solitons admit a warped product structure with a one-dimensional base and space form fibers.
Alshehri et al. (Fri,) studied this question.