Gatsby has gone to a great deal of trouble to create a persona of a wealthy successful man deserving of respect, and he did this all to win back Daisy Buchanan. But in order to have her, they have to carry on an adulterous affair. In Gatsby's mind, his efforts to create an elaborate public persona with a grand house and lavish lifestyle clashes with the necessity of keeping his affair with Daisy a secret. His personal pride and sense of accomplishment are severely compromised as a result.
Gatsby might also experience an inner conflict due to the simple fact that Daisy's failure to wait for him to make his fortune means she is perhaps not really worthy of him. His own strength of character contrasts strongly with Daisy's own comparative weakness and dependency. Daisy is not good enough for Gatsby, but Gatsby's whole life has been about winning her, and the dream of marrying the rich girl he could not have.
Gatsby has an scary resolution as a result of his relationship with Daisy. I think the conflict that you could argue Gatsby now has is that he further drops all inhibition because of his relationship with Daisy. He stops the parties (a representation of people he cared for previously), he fires his staff (they knew too much), and he allows her to kill another human and all he can worry about is how she feels about it. His conflict is that he has completely lost a moral conscience.
Gatsby, in The Great Gatsby, is single-minded and totally dedicated to recapturing his relationship with Daisy. He is obsessed. So there certainly isn't any internal conflict concerning his goal, etc.
Any internal conflict one sees in Gatsby would have to be between want he wants and what he doesn't have. He totally wants Daisy, but she was stolen, in his mind, by somebody else, and he can't have her.
He spends five years of his life searching for her and preparing himself and his image in an attempt to win her back. That is the conflict that Gatsby faces concerning Daisy.