For PRNU-based forensic detectors, the fundamental test statistic is the normalized correlation between the camera fingerprint and the noise residual extracted from the image in successive overlapping analysis windows. The correlation predictor plays a crucial role in the performance of all such detectors. The traditional correlation predictor is based on predefined hand-crafted features representing intensity, texture and saturation characteristics of the image block under inspection. The performance of such an approach depends largely on the training and test data. We propose a convolutional neural network (CNN) architecture to predict the correlation from image patches of suitable size fed as input. Our empirical finding suggests that the CNN generalizes much better than the classical correlation predictor. With the CNN, we could operate with a common network architecture for various digital camera devices as well as a single network that could universally predict correlations for content from all cameras we experimented with, even including the ones that were not used in training the network. Integrating the CNN with our forensic detector gave state-of-the-art results.