Edge-caching is recognized as an efficient technique for future wireless cellular networks to improve network capacity and user-perceived quality of experience. Due to the random content requests and the limited cache memory, designing an efficient caching policy is a challenge. To enhance the performance of caching systems, an accurate content request prediction algorithm is essential. Here, we introduce a flexible model, a Poisson regressor based on a Gaussian process, for the content request distribution in stationary environments. Our proposed model can incorporate the content features as side information for prediction enhancement. In order to learn the model parameters, which yield the Poisson rates or alternatively content popularities, we invoke the Bayesian approach which is very robust against over-fitting. However, the posterior distribution in the Bayes formula is analytically intractable to compute. To tackle this issue, we apply a Monte Carlo Markov Chain (MCMC) method to approximate the posterior distribution. Two types of predictive distributions are formulated for the requests of existing contents and for the requests of a newly-added content. Finally, simulation results are provided to confirm the accuracy of the developed content popularity learning approach.