Uniform magnetic fields are desired in a wide range of applications. The most known device achieving such a purpose is the pair of Helmholtz coils. It consists of two identical circular coils, with their main axis aligned and placed at a distance equal to their common radius from each other. The goal of this research is to find another arrangement of the coils in space so as to achieve the largest region possible with a uniform magnetic field. A topology optimization framework is developed for this purpose. It investigates the ideal distribution of current densities in an axisymmetric 2D domain. The designed topology provides a significant improvement of the volume with a uniform field, which is 6.37 times larger than the reference one obtained with Helmholtz coils.