T2* mapping can be used to characterize tumour hypoxia, which is associated with therapy resistance. We show the feasibility of fast T2* mapping in prostate cancer patients on a 1.5T MR-Linac. The undersampled data was reconstructed by combining parallel imaging and a sparsifying transform with an iterative model-based reconstruction. The method was tested on a multi-compartment phantom and two prostate cancer patients with retrospective undersampling. With the proposed method T2* maps can be acquired in under five minutes. We demonstrated the feasibility of daily quantitative MRI over the course of radiotherapy on an MR-Linac, to characterize treatment response.