The two novels do not exactly parallel each other, but a link between them is that each is centrally concerned with a love affair. In Gatsby, Daisy and Gatsby fall in love briefly before he goes off to fight in World War I. In Normal People, Marianne and Connell fall in love in high school and have a secret affair.
In both novels, the female character is richer than the male: part of Gatsby's love for Daisy resides in how she represents to him the ease and confidence of always having had money. In Normal People, the dynamic is somewhat different. At first, even though Connell's mother works for Marianne's mother as a cleaning lady, it is the more popular Connell who has the ease and confidence that Marianne lacks—and Connell wants to keep the relationship secret. Later, however, Connell is the one who feels ill at ease with Marianne and her richer friends at Trinity College.
In both novels, though the lovers break up, they eventually find each other again. In both, the female gets involves with an abusive man—Marianne is also plagued by an abusive brother named Alan. Daisy puts up with Tom's brutality and affairs.
A difference between the two books, however, is that while Marianne and Connell are able to reunite in a supportive way and Marianne is able to start growing away from abusive relationships, Daisy ends up back with Tom.