Various types of indices for estimating functional connectivity have been developed over the years that have introduced effective approaches to discovering complex neural networks in the brain. Two significant examples are the phase lag index (PLI) and transfer entropy (TE). Both indices have specific benefits; PLI, defined using instantaneous phase dynamics, achieves high spatiotemporal resolution, whereas transfer entropy (TE), defined using information flow, reveals directed network characteristics. However, the relationship between these indices remains unclear. In this study, we hypothesize that there exists a complementary relationship between PLI and TE to discover new aspects of functional connectivity that cannot be detected using either PLI or TE. To validate this hypothesis, we evaluated the synchronization in a coupled Rössler model using PLI and TE. Consequently, we proved the existence of non-linear relationships between PLI and TE. Both indexes exhibit a specific trend that demonstrates a linear relationship in the region of small TE values. However, above a specific TE value, PLI converges to a constant irrespective of the TE value. In addition to this relational difference in synchronization, there is another characteristic difference between these indices. Moreover, by virtue of its finer temporal resolution, PLI can capture the temporal variability of the degree of synchronization, which is called dynamical functional connectivity. TE lacks this temporal characteristic because it requires a longer evaluation period in this estimation process. Therefore, combining the advantages of both indices might contribute to revealing complex spatiotemporal functional connectivity in brain activity.