In this paper, we deeply investigate the phase evolution and the underlying topological vector potential in the nonlinear interference of solitons. Based on the double-soliton solution of 1D nonlinear Schrödinger equation, we find that the density zeros of wave function generally exist in the extended complex space, each density zero corresponds to the vector potential produced by Dirac magnetic monopole. The vector potential field is composed of periodically distributed Dirac magnetic monopole pairs with opposite magnetic charges. By observing the motion of magnetic monopoles, we can conveniently understand the phase evolution characteristics during the interference process. In particular, we find that the collision of a pair of magnetic monopoles with opposite charge on the real axis corresponds exactly to the $ \pm\pi $ jump of the wave function phase at nodes. For comparison, we also discuss Dirac magnetic monopoles and vector potential field in linear wave packet interference case. The results show that the Dirac magnetic monopole potential widely exists in the interference phenomena of wave fields, and the distribution of magnetic monopoles in the extended complex space can be used to distinguish the topological properties behind the linear and nonlinear interference process.