In recent years, rumors have been shown to have a significant impact on individual and societal activities. As renewables play an increasingly significant role in electricity markets, certain rumors may deviate the bidding behavior of market entities and eventually affect the performance of market operations. In this study, we attempt to reveal the general threats caused by rumors in the context of day-ahead electricity markets considering the integration of volatile renewables. First, we model the propagation of rumors in the societal system considering the weight of propagation resistance, which principally reflects the communication accessibility of market entities. Second, we develop an integrated two-layer network model to uncover the inherent coupling mechanism between market operations and rumor propagation. In particular, the role of electricity market operations on rumor propagation is characterized by changes in the truthfulness of rumors associated with electricity prices. The rumors, in turn, affect the bidding quantities of market entities in electricity market operations. Finally, numerical experiments are conducted on modified IEEE 6-bus and 118-bus systems. The results demonstrate the potential threats of rumors to electricity market operations with different penetration levels of renewables.