With the recognition that the circulation is strongly coupled with the Indian summer monsoon rainfall (ISMR), a number of large‐scale circulation indices have been proposed to represent the Indian summer monsoon to aid diagnosis of teleconnections with ISMR and evaluation of simulations by climate models. The circulation indices, however, correlate poorly with ISMR raising doubts on the coupling between the two. In this study, we identify reasons behind the poor correlations and estimate a potential limit on this correlation between circulation indices and ISMR. One mechanistic reason for poor correlations between circulation indices and ISMR is that the period and variance explained by the oscillatory modes of circulation indices differ significantly from those of ISMR leading to their phases also differing between modes of circulation indices and corresponding modes of ISMR. Further, the wind anomaly patterns associated with wind indices project strongly on the climatological monsoon circulation unlike that associated with the ISMR, another reason for their poor correlation with ISMR. As a result, all circulation indices underestimate the negative correlation between June–September sea‐surface temperature (JJAS SST) over the Niño3.4 and ISMR and fail to simulate the lead–lag relationship between the two. A conservative estimate of the interannual variance explained by coupling of the JJAS rainfall over continental India and winds in the neighbourhood is strong, explaining about 55% variance distributed in three leading coupled modes. Therefore, the effectiveness of any circulation indices in explaining the ISMR variance is potentially limited to that associated with the dominant mode (∼30%). The local response of winds to deep convection over the waters of the Indian Ocean and western Pacific warm pool leads to a strong increasing trend in some of the circulation indices and adds “noise” modes contributing to the de‐correlation between circulation indices and ISMR.