To talk about something in a loose or gossipy manner. A noun or pronoun can be used between "blab" and "around." They are blabbing around that story as if it's the truth. Management is just casually blabbing around the idea of layoffs. Don't blab that nonsense around here, we're not buying it.
blab something around
Inf. to gossip something to others; to spread some news or secret. It's true, but don't blab it around. Did you blab around everything I told you to keep to yourself?