Time Machine on internal disk when booting on external SSD

Hi, on my iMaC, I am now using external SSD with USB 3 as system disk (and not internal disk anymore). I would like to use the now not-used-anymore internal disk for Time Machine backups now. But TM doesn't show internal disk when I ask to choose a backup disk.

Do you know how to fix this ? I have 1 TB available, it would be a pity not using it for backups...

Thank you,

Fab