According to what I’ve seen, Arcana clerics, wizards, bards (through the Magical Secrets feature), and sorcerers are the only classes/subclasses that can learn or prepare the wish spell.
Are there any other options available to be able to cast the wish spell as a caster, without using magic items?
Best Answer
You've pretty much got them covered
Wish only appears on the wizard and sorcerer spell list, and the only other classes that can access those spell lists for level 9 spells are the bard through Magical Secrets and the Arcana Domain of the cleric.
The only other way for a character to gain the effect of wish is through Divine Intervention. This cleric feature says:
Wish could be chosen as the nature of the intervention (in fact, it can even be a domain spell to Arcana Domain clerics via the Arcane Mastery feature, a distinction explored by this question)