This is a really interesting question. The reason why the answer isn't so easy to figure out is because we have to filter Gatsby through the lens of the 1920s. I could talk all day about the huge amount of "Gatsby gossip" that is in the novel before this actual moment, but we have to wait (and wait) until the middle of chapter 4 to hear it from Gatsby. The flappers and gangsters at Gatsby's parties get in the way.
In fact, the first time we hear something from Gatsby's lips, he says, "My family all died, and I came into a great deal of money." Of course Gatsby first insists that San Francisco is part of the Midwest. Um, San Francisco is absolutely not the Middle West. But I love the use of wording here to avoid a lie, per se. Yes, his family died. Yes, he came in to a great deal of money. What he doesn't say is that he didn't come into the money because his family died. Nick, of course, mistakenly takes Gatsby's statement as a statement of inheritance.
Awww, our little innocent Nick.
There's another little inkling a bit later when Gatsby tries to tactlessly ask Nick to go into business saying, "I carry on a little business on the side, a sort of side line, you understand." Uh huh. Obviously if Gatsby scoffs at Nick being a bond man and then offers him this "job," then this is a way to make money. How would Gatsby have know this was a way to make money if he didn't make money that way himself? But are there specifics here? No.
Even later, Gatsby "clarifies" the situation with Nick:
"I thought you inherited your money."
"I did, old sport," he said automatically, "but I lost most of it in the big panic--the panic of the war. ... Oh, I've been in several things," he corrected himself. "I was in the drug business and then I was in the oil business. But I'm not in either one now."
And yet, even when Tom confronts Gatsby about his bootlegging, Gatsby responds by saying, "What about it?" This is even after Tom mentions Chase taking the fall for Gatsby. So, of course, Gatsby continues to be the king of circumlocution, as esoteric as ever. Gotta love those well-dressed, handsome rich guys who revel in word play.