In this work, the micro-macro approach is used to simulate the flow of dilute polymer solutions by means of a kinetic model coupled with the dynamics of a transient network. The transient network modeling is based on the original formulation, in which the kinetics of microstates describes the complexity of interactions among the macromolecules suspended in a Newtonian solvent (Rincn et al, J Non-Newton Fluid 131:64-77, 2005). The average concentration of microstates, at a given time, defines a variable maximum segment length (variable extensibility) of the molecular FENE model. The non-Newtonian contribution to the extra stress tensor is computed according to the Brownian configuration-fields method. Comparisons with the Oldroyd-B model validates its limiting behavior. Numerical results show the influence of the solvent to total viscosity ratio and shear rate, on the transient and steady rheological phenomena of complex fluids with microstates.