You can ask someone not to say something, however, sometimes it has the opposite affect. They feel it's a juicy tidbit of gossip so they feel inclined to share.
My mom went to the bar and saw my neighbor, the next day he saw my bro and said he saw my mom getting drunk. My bro said it was non of his business and he didn't care. I sometimes flirt with the neighbor, how should I tell him not to gossip?