Machine learning methods have revolutionized studies in several areas of knowledge, helping to understand and extract information from experimental data. Recently, these data-driven methods have also been used to discover structures of mathematical models. The sparse identification of nonlinear dynamics (SINDy) method has been proposed with the aim of identifying nonlinear dynamical systems, assuming that the equations have only a few important terms that govern the dynamics. By defining a library of possible terms, the SINDy approach solves a sparse regression problem by eliminating terms whose coefficients are smaller than a threshold. However, the choice of this threshold is decisive for the correct identification of the model structure. In this work, we build on the SINDy method by integrating it with a global sensitivity analysis (SA) technique that allows to classify terms according to their importance in relation to the desired quantity of interest. The proposed SINDy-SA approach thus eliminates the need to define the SINDy threshold. We compare our method with the original SINDy approach employing them in a variety of applications whose simulated data have different behaviors. For each application, we formulate different experimental settings and select the best model for both methods using model selection techniques based on information criteria. The results demonstrate that the SINDy-SA framework is a promising methodology to accurately identify interpretable data-driven models.