When you want to have a relaxed and intimate conversation with someone, you might use the phrase "cosy chat" to describe it. However, if you're looking for alternative words or phrases to describe this kind of interaction, there are plenty of options to choose from. You could say you want to have a heart-to-heart, a friendly chat, a confab, a chinwag, or a tete-a-tete. These synonyms convey the sense of warmth, comfort, and familiarity that comes with a cosy chat, and can help you to express yourself more precisely when discussing your desire for a meaningful conversation with someone you care about.