'muse-like' originates from Modern English, formed from 'muse' + the suffix '-like', where '-like' meant 'having the characteristic of'.

'muse' entered English via Old French 'muse' from Latin 'musa', ultimately from Greek 'Μοῦσα (Mousa)'; the compound 'muse-like' was formed later in Modern English by combining 'muse' with the productive suffix '-like'.

Initially 'Mousa' referred to one of the Muses (goddesses of the arts); over time 'muse' came to mean a source of artistic inspiration, and with '-like' the compound came to mean 'resembling or acting as a muse'.