Additive manufacturing technologies present a series of advantages such as high flexibility, direct CAD to final product fabrication, and compact production techniques which make them an attractive option for fields ranging from medicine and aeronautics to rapid prototyping and Industry 4.0 concepts. However, additive manufacturing also presents a series of disadvantages, the most notable being low dimensional accuracy, low surface quality, and orthotropic mechanical behaviour. These characteristics are influenced by material properties and the process parameters used during manufacturing. Therefore, a predictive model for the characteristics of additive manufactured components is conceivable. This paper proposes a study on the feasibility of implementing Deep Neural Networks for predicting the dimensional accuracy and the mechanical characteristics of components obtained through the Fused Deposition Modelling method using empirical data acquired by high precision metrology. The study is performed on parts manufactured using PETG and PLA materials with known process parameters. Different Deep Neural Network architectures are trained using datasets acquired by high precision metrology, and their performance is tested by comparing the mean absolute error of predictions on training and validation data. Results show good model generalisation and convergence at high accuracy, indicating that a predictive model is feasible.