Network security data generally consists of hundreds of counters periodically collected in the form of time-series, resulting in a complex-to-analyze multivariate time-series (MTS) process. We investigate a novel approach to time-series modeling, inspired by the successes of large pre-trained foundation models. We introduce FAE (Foundation Auto-Encoders), a foundation generative-AI model for anomaly detection in time-series data, based on Variational Auto-Encoders (VAEs). By foundation, we mean a model pre-trained on massive amounts of time-series data which can learn complex temporal patterns useful for accurate modeling, forecasting, and detection of anomalies on previously unseen datasets. Based on the DC-VAE architecture originally designed for multivariate anomaly detection, FAE leverages VAEs and Dilated Convolutional Neural Networks (DCNNs) to build a generic model for univariate time-series modeling, which could eventually perform properly in out-of-the-box, zero-shot anomaly detection applications. We introduce the main concepts and ideas of this foundation model, and present some preliminary results in a multi-dimensional network monitoring dataset, collected from an operational mobile Internet Service Provider (ISP). This work represents a significant step forward in the development of foundation generative-AI models for anomaly detection in time-series analysis, with applications spanning cybersecurity, network management, and beyond.