Nick didn't identify with Gatsby in every way, but he did know of similarities and found a kinship with him because of these and because of Gatsby's pure idealism.
Both Nick and Gatsby/Gatz are from rural beginnings (Nick from the Midwest and Gatz from North Dakota and then Minnesota). At the beginning of the novel, Nick remarks that he is proud of his honesty and his ability to withhold judgment of other people. Although he does do so outwardly, for the most part, the reader does learn (via Nick's thoughts) how Nick feels about the other characters. Nick initially dislikes Tom and clearly despises him by the end of the novel. Nick appreciates Daisy's beauty but recognizes an air of superficiality in her lifestyle (as noted by Gatsby himself that her "voice is full of money").
Nick seems to take to Jordan, but as laid back and liberated as she is, he doesn't make a profound connection to her.
Nick does admire Gatsby. Nick identifies with him in that they have similar beginnings and both had transplanted to the East. While Nick does not really approve of Gatsby's involvement with organized crime or of his flamboyant parties, Nick does come to admire Gatsby's romantic idealism, his naive hope in a seemingly impossible American Dream. So, while Nick might not necessarily completely identify with Gatsby and all of his motives, he does admire him much more than any of the other people he's met in the East. This is why, in Chapter 8, Nick tells him:
"They’re a rotten crowd,” I shouted across the lawn. “You’re worth the whole damn bunch put together.”
I’ve always been glad I said that. It was the only compliment I ever gave him, because I disapproved of him from beginning to end. First he nodded politely, and then his face broke into that radiant and understanding smile, as if we’d been in ecstatic cahoots on that fact all the time.
Nick didn't approve of Gatsby, but he identified his own (Nick's) honesty with the purity of Gatsby's romanticized dream. It is no surprise then, in the end, that Nick goes to great lengths to summon people to Gatsby's funeral. Clearly, all of Gatsby's so called friends and associates had just been using Gatsby for connections and parties. Nick had at least come to identify with Gatsby as his only real friend.
In Chapter 1, Nick relates that it wasn't Gatsby himself that he disapproved of; it was his surroundings. And Nick also expresses his admiration for Gatsby's spirit, something which can't be faked, even by someone posing as someone else:
. . . it was an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again. No—Gatsby turned out all right at the end; it is what preyed on Gatsby, what foul dust floated in the wake of his dreams that temporarily closed out my interest in the abortive sorrows and short-winded elations of men.