Can machines design? Can they come up with creative solutions to problems and build tools and artifacts across a wide range of domains? Recent advances in the field of computational creativity and formal Artificial General Intelligence (AGI) provide frameworks for machines with the general ability to design. In this paper we propose to integrate a formal computational creativity framework into the Gödel machine framework. We call the resulting framework design Gödel machine. Such a machine could solve a variety of design problems by generating novel concepts. In addition, it could change the way these concepts are generated by modifying itself. The design Gödel machine is able to improve its initial design program, once it has proven that a modification would increase its return on the utility function. Finally, we sketch out a specific version of the design Gödel machine which specifically addresses the design of complex software and hardware systems. Future work aims at the development of a more formal version of the design Gödel machine and a proof of concept implementation.