Ongoing fluctuations in prestimulus neural excitability and connectivity patterns influence near-threshold detection, or whether or not a stimulus is perceived. Do they also influence whether one or another stimulus is perceived? In this Magnetoencepahlography study, we showed participants brief presentations of a bi-stable image consisting of a face superimposed with a house, and asked them to report which of the two contents of the image they perceived on each trial. Multivariate pattern analysis revealed that perceiving bi-stable faces and houses shared common neural substrates with perceiving unambiguous faces and houses. After source localizing the post-stimulus signals to the FFA, we analyzed oscillatory power and connectivity in FFA during a prestimulus interval. We found no differences in FFA power, but we did find differences in FFA connectivity prior to face vs house reports. Specifically, local graph theoretical measures showed that in the alpha frequency range (8-13 Hz), FFA was more efficiently and robustly connected to the rest of cortex prior to face reports. These prestimulus connectivity measures additionally predicted the accuracy of post-stimulus decoding. Our work suggests that object perception is shaped by ongoing network states captured with connectivity measures.