Under remote anti-plane shear stresses and in-plane magnetoelectric loads, the magnetoelectroelastic coupling interaction between a generalized screw dislocation and a circular inhomogeneity with an imperfect interface in transversely isotropic magnetoelectroelastic solids is investigated. The generalized screw dislocation may be at any point of the inhomogeneity and is subjected to a point force, a point charge and a line electric current at the core. By means of a complex-variable method, the analytic solutions of magnetoelectroelastic fields are obtained. With the aid of the generalized Peach-Koehler formula, the explicit expressions of image forces exerted on the piezoelectric screw dislocations are derived. The influence of the interface imperfection on the magnetoelectroelastic fields inside the inhomogeneity is studied. The image force acting on the generalized screw dislocation near the imperfect interface is also discussed for variable parameters (interface imperfection, material magnetoelectroelastic mismatch and dislocation position). These basic solutions can be used as Green′s functions for the analysis of the corresponding crack problem in magnetoelectroelastic solids.