The Orientated Tessellation Updating Method (OTUM) is a fast mesoscopic model of grain growth that has been published recently for a single phased metal without diffusion or segregation of alloying elements. It is based on tessellation techniques and simple linear algebra. On this basis, some ideas to develop an upscaling strategy are broached in this work. The aim is to develop a macroscopic model of grain growth whose state variables contain for each material point the statistical descriptors of the microstructure (e.g., disorientation, grain size and shape distributions).