Dielectric Elastomers (DE) represent an attractive technology for the realization of mechatronic actuators, due to their lightweight, high energy density, high energy efficiency, scalability, and low noise features. In order to produce a stroke, a DE membrane needs to be pre-loaded with a mechanical biasing mechanism. In our previous works, we compared the stroke achieved with different biasing mechanisms for a circular out-of-plane DE Actuator (DEA), i.e., hanging masses, linear and bi-stable springs. The novel contribution of this paper is the investigation of a biasing design approach based on permanent magnets. The resulting magnet-based actuators are usually more compact than the spring-based ones, allowing to obtain more compact systems. Two design solutions are proposed and compared, namely a first one characterized by a stable actuation, and a second one which permits to achieve a higher stroke, but it is intrinsically unstable. The effectiveness of the novel design solution is assessed by means of several experiments.