They do have that conversation, or something very similar to it, ingame. It happens in the Orphanage in Centra, after they rescue Rinoa in Esthar.
Squall: It was just a dream... It doesn't mean anything. Don't worry
about it.
Rinoa: ...I guess you're right.
Squall: How about this... I'll be here...
Rinoa: ...Why?
Squall: The reason why you couldn't find me was because we haven't
promised yet.
Rinoa: Promised...?
Squall: I'll be waiting for you. If you come here, you'll find me. I
promise.
Rinoa: I'll be here, too. It's a promise! Thanks, Squall! Next time,
we'll meet for sure!
So, basically, everything with a question mark is Rinoa, and the rest is Squall.