In Chapter Four of Fitzgerald's The Great Gatsby, Gatsby says to Nick,
Look here, old sport,...What's your opinion of me anyhow?....Well, I'm going to tell you something about my life....I don't want you to get a wrong idea of me from all these stories you hear.
Gatsby asks Nick what he thinks of him so that he can tell his life story in order to prevent Nick's believing the rumors about him. He says to Nick, "This is the God's truth." Gatsby wants Nick to think well of him. This is why he asks Nick "What's your opinion of me anyhow?"
It is after finishing his own personal history, a history that resembles that of the early immigrants, the adventurers of early America who sought "the American Dream," that Gatsby makes his request. He does not ask Nick what he thinks of him in order to make a request because, before doing so, he tells Nick about himself. He does this, not to make the request, but to impress Nick and somewhat endear himself to Nick by recreating an endearing red-blooded American who seeks the Dream. Having endeared himself to Nick will lessen the likelihood of Nick's refusing his request:
'I'm going to make a big request of you today,' he said, pocketing his souvenirs with satisfaction,' so I thought you ought to know something about me. I didn't want you to think I was just some nobody. You see I usually find myself among strangers because I drift here and there trying to forget the sad thing that happened to me.'