Early in the novel, Jay Gatsby is a man of mystery. The other characters are fascinated by his glamor, wealth, and aloofness. Because they are unaware of his actual history, they try to come up with theoretical backstories that match up with Gatsby's carefully curated image. However, a few lines from these characters does provide some clues as to his true background and motivations, though they are often tinged with irony and half-truths.
During Gatsby's party in chapter 3, several of the guests surmise about Gatsby's background. One woman believes he is a murderer on the run:
You look at him sometimes when he thinks nobody's looking at him. I'll bet he killed a man.
While later revelations show that Gatsby did not kill anyone, the guest is correct in her belief that he is hiding something from others, though it is not as sensationalist as she presumes.
Of course, some of the rumors about Gatsby do foreshadow his true background, such as this one from the start of chapter 4:
"He's a bootlegger," said the young ladies, moving somewhere between his cocktails and his flowers. "One time he killed a man who had found out that he was nephew to Von Hindenburg and second cousin to the devil ..."
As it turns out, Gatsby is a bootlegger, though he hardly fits the romantic image projected here. He is not related to any European aristocrats or American "old money" (the de facto aristocracy of the United States). Instead, he comes from the lower classes.
Later in chapter 4, Meyer Wolfsheim's statements about Gatsby's character also betray a lack of understanding of the man:
Yeah, Gatsby's very careful about women. He would never so much as look at a friend's wife.
Obviously, anyone who has read The Great Gatsby knows this is not true, since Gatsby's dearest hope is that his wealth will convince Daisy to leave her husband.