Functional connectivity refers to covarying activity between spatially segregated brain regions and can be studied by measuring correlation between functional magnetic resonance imaging (fMRI) time series. These correlations can be caused either by direct communication via active axonal pathways or indirectly via the interaction with other regions. It is not possible to discriminate between these two kinds of functional interaction simply by considering the covariance matrix. However, the non-diagonal elements of its inverse, the precision matrix, can be naturally related to direct communication between brain areas and interpreted in terms of partial correlations. In this paper, we propose a Bayesian model for functional connectivity analysis which allows estimation of a posterior density over precision matrices, and, consequently, allows one to quantify the uncertainty about estimated partial correlations. In order to make model estimation feasible it is assumed that the sparseness structure of the precision matrices is given by an estimate of structural connectivity obtained using diffusion imaging data. The model was tested on simulated data as well as resting-state fMRI data and compared with a graphical lasso analysis. The presented approach provides a theoretically solid foundation for quantifying functional connectivity in the presence of uncertainty.