Out-of-field patient doses in proton therapy are dominated by neutrons. Currently, they are not taken into account by treatment planning systems. There is an increasing need to include out-of-field doses in the dose calculation, especially when treating children, pregnant patients, and patients with implants. In response to this demand, this work presents the first steps towards a tool for the prediction of out-of-field neutron doses in pencil beam scanning proton therapy facilities. As a first step, a general Monte Carlo radiation transport model for simulation of out-of-field neutron doses was set up and successfully verified by comparison of simulated and measured ambient neutron dose equivalent and neutron fluence energy spectra around a solid water phantom irradiated with a variation of different treatment plan parameters. Simulations with the verified model enabled a detailed study of the variation of the neutron ambient dose equivalent with field size, range, modulation width, use of a range shifter, and position inside the treatment room. For future work, it is planned to use this verified model to simulate out-of-field neutron doses inside the phantom and to verify the simulation results by comparison with previous in-phantom measurement campaigns. Eventually, these verified simulations will be used to build a library and a corresponding tool to allow assessment of out-of-field neutron doses at pencil beam scanning proton therapy facilities.