Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study the brain function. The selection of the proper number of signals of interest is an important step in the analysis to reduce the risk of over/underfitting. The inherent sample dependence in the spatial or temporal dimension of the fMRI data violates the assumption of independent and identically distributed (i.i.d.) samples and limits the usefulness of the practical formulations of information-theoretic order selection criteria. We propose a novel method using an entropy rate matching principle to mitigate the effects of such sample dependence in order selection. We perform order selection experiments on the simulated fMRI data and show that the incorporation of the proposed method significantly improves the accuracy of the order selection by different criteria. We also use the proposed method to estimate the number of latent sources in fMRI data acquired from multiple subjects performing a visuomotor paradigm. We show that the proposed method improves the order selection by alleviating the over-estimation due to the intrinsic smoothness and the effect of smooth preprocessing on the fMRI data.