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This paper is concerned with learning transferable forward models for push manipulation that can be applying to novel contexts and how to improve the quality of prediction when critical information is available. We propose to learn a parametric internal model for push interactions that, similar for humans, enables a robot to predict the outcome of a physical interaction even in novel contexts. Given a desired push action, humans are capable to identify where to place their finger on a new object so to produce a predictable motion of the object. We achieve the same behaviour by factorising the learning into two parts. First, we learn a set of local contact models to represent the geometrical relations between the robot pusher, the object, and the environment. Then we learn a set of parametric local motion models to predict how these contacts change throughout a push. The set of contact and motion models represent our internal model. By adjusting the shapes of the distributions over the physical parameters, we modify the internal model's response. Uniform distributions yield to coarse estimates when no information is available about the novel context (i.e. unbiased predictor). A more accurate predictor can be learned for a specific environment/object pair (e.g. low friction/high mass), i.e. biased predictor. The effectiveness of our approach is shown in a simulated environment in which a Pioneer 3-DX robot needs to predict a push outcome for a novel object, and we provide a proof of concept on a real robot. We train on 2 objects (a cube and a cylinder) for a total of 24,000 pushes in various conditions, and test on 6 objects encompassing a variety of shapes, sizes, and physical parameters for a total of 14,400 predicted push outcomes. Our results show that both biased and unbiased predictors can reliably produce predictions in line with the outcomes of a carefully tuned physics simulator.