This paper investigates prospects of utilizing a high-power laser-driven target-normal-sheath-acceleration proton beam for the experimental demonstration of the magnetic self-focusing phenomenon in charged particle beams. In the proposed concept, focusing is achieved by propagating a space-charge dominated ion beam through a stack of thin conducting and grounded foils separated by vacuum gaps. As the beam travels through the system, image charges build up at the foils and generate electric field that counteracts the beam's electrostatic self-field — a dominant force responsible for expansion of a high current beam. Once the electrostatic self-field is “neutralized” by the image charges, the beam currents magnetic self-field will do the focusing. The focal spot size and focal length depends on the choice of a number of foils and distance between foils. Considering the typical electrical current level of a target-normal-sheath-acceleration proton beam, we conclude that it is feasible to focus or collimate a beam within tens of millimeters distance, e.g., using 200–1000 Al foils, 0.5 µm thick each, with foil spacing ranging from 25 µm to 100 µm. These requirements are within technical capabilities of modern target fabrication, thus allowing the first possible demonstration of the pinch effect with heavy ion beams.