We consider in this article a model of vesicle moving into a viscous incompressible fluid. The vesicle is described through a phase-field equation and through a transport equation modeling the local incompressibility of its membrane. The equations for the fluid are the classical Navier--Stokes equations with a force resulting from the presence of the vesicle. The model for the system vesicle--fluid is an approximation of a model obtained by Jamet and Misbah. Our main result states the existence of weak solutions for the corresponding system. The proof is based on compactness/monotonicity arguments