The development of increasingly complex computer architectures has led to the implementation of parallelization strategies specifically aimed at reducing the runtime of simulations. In the context of poromechanics, several problems involve an evolutionary process that could potentially be addressed using parallel-in-time techniques. In this work, we explore this possibility for the quasi-static Biot's consolidation model, which governs the interaction between fluid flow and deformation in porous media. The resulting system of equations is linear and fully coupled, and its two-field formulation considers fluid pressure and displacement as the primary unknowns. Common solvers for this problem include fully implicit (i.e., monolithic) methods and iterative coupling schemes. While the former require the simultaneous solution of all the unknowns, the latter involve solving one of the subsystems first, followed by the solution of the other. An example of such an approach is the fixed-stress method. In recent years, the relatively slower evolution of the mechanical component compared to the flow equation has motivated the introduction of the so-called multirate approach. This family of methods enhance iterative coupling schemes by employing two different time scales for the two subsystems of the problem, reducing the computational cost. The main contribution of this work lies in the application of the parallel-in-time Parareal algorithm to the numerical integration of the Biot's model, using the fixed-stress and multirate fixed-stress schemes as the propagators within the algorithm. The convergence of the resulting solvers is studied both analytically and numerically, providing explicit conditions that guarantee the convergence of the proposed methods.