The answer to this question involves one of the most often quoted passages of the novel: "Her voice is full of money."
Throughout the novel, Nick has been entranced by Daisy's voice. Even though many of her attempts at conversation seem inane, her voice is entrancing. In Chapter 1, Nick responds to Daisy's comment that he was like a rose. Nick disagrees with this comparison, but he admits that "a stirring warmth flowed from her as if her heart was trying to come out to you concealed in one of those breathless, thrilling words." But by the end of the chapter, Nick is no longer intrigued by her voice.
In Chapter 7, Nick tries to describe Daisy's voice to Gatsby. He calls it "indiscreet." But he cannot be any more specific than this. It is Gatsby, surprisingly, who recognizes the source of its charm: it is the voice of money. It is this voice and all its starshine that attracted Gatsby to Daisy in the first place. Daisy has always had money. She came from a wealthy family; she married an even wealthier husband. This type of lifestyle exudes in her manner and her voice. She has never known sacrifice; she has never had to do without.
Gatsby who has known what it is like to not have everything he wants recognizes very clearly one who has and who always had it all. This is what Gatsby wants as well. But no matter how hard he tries, Gatsby's voice will never be full of money. As a newly rich man, he can only pretend to speak as he believes the wealthy speak. But he does not speak as someone does who has known money his entire life.
Nick comes from a fairly well-to-do family himself. So he cannot quite pinpoint the source of Daisy's charm--at least not until Gatsby names it. The desire to speak like that, to acquire the mannerisms of the very rich, is not what Nick tries to assume. He is somewhat privileged and is only mildly curious about those who are more privileged that he.