A Monk following the Way of the Four Elements can use Elemental Disciplines. Some of them are actually spells:

Some elemental disciplines allow you to cast spells (PHB 80)

However they are not spellcasters, as evident from the multiclassing section, not even like Eldritch Knights or Arcane Tricksters.

The Monk does not have to have material components, but what about somatic components? If I multiclass into Druid, can I cast these spells while in Wild Shape?