Daisy's insistence that the rumor of Nick's engagement is true despise his denial suggests a conflict between possibly her and Gatsby, or more importantly is could just be hinting at a parallel between Nick and Gatsby. Considering that they both left the Midwest to live in New York because of woman. Nick, clearly trying to run away from a woman and Gatsby obviously pursuing one (aka Daisy). As for the suggestion of a conflict, the only one that possibly makes sense is that Daisy is mad at Nick because he's been away for so long, and is just now deciding to live near his family, considering they're cousins. So, in a matter of speaking she's playfully ridiculing him while also trying to figure out why he's been gone so long.
