Effective models of crystallographic texture development during thermomechanical processing can help speed up the introduction of new alloys, optimise current processing routes and catalyse new process development. Texture prediction models of varying complexity have been proposed, ranging from simple homogenised models to full-field crystal plasticity (CP) models. Although the latter can account for variation of microstructure and its development during processing more accurately, they are computationally expensive, and cannot be run in-line within forming process models or used to probe uncertainty arising from varied input parameters. Their computational expense also makes it prohibitive to make predictions of the spatial distribution of texture in large components, which requires many calls to the CP model with very similar inputs. In this work, we have used Gaussian Processes (GP) to make texture predictions during a forging process. A GP can be used to create surrogate models within a known region of parameter space, in order to reduce the number of calls to the underlying physical model. Whereas a typical GP is trained using data from a single source, a kernel function can be produced to allow latent correlations between training data of different fidelity and sparsity in parameter space. These different fidelities could be the CP models mentioned but equally experimental observations. In the model presented here, the texture is represented by an orientation distribution function (ODF) parametrised using harmonic functions and is both an input and output. Temperature and loading condition vary throughout the forging and are also inputs to the GP and physical models. We find that the GP can produce textures consistent with the CP models within the uncertainty introduced by the finite sampling of the ODF. Careful consideration was taken to minimise both the dimension and size of the parameter space to ensure the surrogate was efficient for large training sets. The GP is orders of magnitude quicker than the complex CP models and will allow an effective coupling of physical and process models.