Compressed sensing applied to magnetic resonance imaging (MRI) allows to reduce the scanning time by enabling images to be reconstructed from highly undersampled data. In this paper, we tackle the problem of designing a sampling mask for an arbitrary reconstruction method and a limited acquisition budget. Namely, we look for an optimal probability distribution from which a mask with a fixed cardinality is drawn. We demonstrate that this problem admits a compactly supported solution, which leads to a deterministic optimal sampling mask. We then propose a stochastic greedy algorithm that (i) provides an approximate solution to this problem, and (ii) resolves the scaling issues of [1, 2]. We validate its performance on in vivo dynamic MRI with retrospective undersampling, showing that our method preserves the performance of [1, 2] while reducing the computational burden by a factor close to 200. Our implementation is available at https://github.com/t-sanchez/stochasticGreedyMRI.