It's possible, but my impression is that no MMU makes it difficult. Here is an example [1] of Linux on a Cortex M4 (a very boring STM32F4XX)
[1] https://www.cs.cmu.edu/~awb/linux.history.html
[2] https://en.wikipedia.org/wiki/ΜClinux
[3] https://www.eetimes.com/how-uclinux-provides-mmu-less-proces...