Reasoning over the interplay between object deformation and force transmission through contact is central to the manipulation of compliant objects. In this paper, we propose Neural Deforming Contact Field (NDCF), a representation that jointly models object deformations and contact patches from visuo-tactile feedback using implicit representations. Representing the object geometry and contact with the environment implicitly allows a single model to predict contact patches of varying complexity. Additionally, learning geometry and contact simultaneously allows us to enforce physical priors, such as ensuring contacts lie on the surface of the object. We propose a neural network architecture to learn a NDCF, and train it using simulated data. We then demonstrate that the learned NDCF transfers directly to the real-world without the need for fine-tuning. We benchmark our proposed approach against a baseline representing geometry and contact patches with point clouds. We find that NDCF performs better on simulated data and in transfer to the real-world.