Could Nick Carraway from The Great Gatsby be seen as a potential gold digger because he only associates with those who have money?

No, one cannot say that Nick is a gold digger or even potentially so. Firstly, his association with the very wealthy Tom and Daisy Buchanan is a result of his kinship with Daisy. She is his cousin and it is, therefore, only natural that he should have a relationship with her. Furthermore, Nick has moved East, which is totally foreign to him, and it is common practice for relatives to seek the company of family or associates when they are in an unfamiliar place.

Secondly, Nick's association with Jay Gatsby, who is fabulously wealthy as well, arose as a matter of chance, as he himself states in chapter one:

It was a matter of chance that I should have rented a house in one of the strangest communities in North America.

This means that he did not rent a house next to Jay Gatsby's on purpose so that he may improve his chance of forming a friendship with him. In fact, Nick only discovered later who his neighbor was. Furthermore, it was Jay who sought his company and not the other way around, as suggested in the following extracts from chapter three:

I believe that on the first night I went to Gatsby’s house I was one of the few guests who had actually been invited.

I had been actually invited. A chauffeur in a uniform of robin’s-egg blue crossed my lawn early that Saturday morning with a surprisingly formal note from his employer: the honor would be entirely Gatsby’s, it said, if I would attend his “little party” that night. He had seen me several times, and had intended to call on me long before, but a peculiar combination of circumstances had prevented it — signed Jay Gatsby, in a majestic hand.

Further evidence that Nick was not a gold digger lies in the fact that when Jay introduced him to Meyer Wolfsheim, the latter confused him with someone who was looking for, as he called it, a 'business gonnegtion.' If Nick had sought wealth, he would have jumped at the first suggestion that there was much money to be made from his association with the gentleman, for he could see that Jay's relationship with him had brought him much wealth, but he did not.

More proof that Nick did not seek wealth because of his association with the rich, is found in the fact that Jay offered him an opportunity to make money, which Nick refused outright. Jay felt that he was returning Nick's favor for arranging his meeting with Daisy. The following extracts from chapter five relate the two men's discussion about the matter:

“I thought you didn’t, if you’ll pardon my — You see, I carry on a little business on the side, a sort of side line, you understand. And I thought that if you don’t make very much — You’re selling bonds, aren’t you, old sport?”

“Trying to.”

“Well, this would interest you. It wouldn’t take up much of your time and you might pick up a nice bit of money. It happens to be a rather confidential sort of thing.”

I realize now that under different circumstances that conversation might have been one of the crises of my life. But, because the offer was obviously and tactlessly for a service to be rendered, I had no choice except to cut him off there.

“I’ve got my hands full,” I said. “I’m much obliged but I couldn’t take on any more work.”

“You wouldn’t have to do any business with Wolfsheim.” Evidently he thought that I was shying away from the “gonnegtion” mentioned at lunch, but I assured him he was wrong. He waited a moment longer, hoping I’d begin a conversation, but I was too absorbed to be responsive, so he went unwillingly home.

Finally, Nick grew to despise the wealthy for their carelessness and would not want to associate with them. In the final chapter, he is quite offhanded with Tom when he meets him after Gatsby's funeral and, on a previous occasion, he had also called them a 'rotten crowd,' just before Gatsby's murder, further suggesting that he did not want to have anything to do with them. His musings in this regard pertinently indicate his scorn:

They were careless people, Tom and Daisy — they smashed up things and creatures and then retreated back into their money or their vast carelessness, or whatever it was that kept them together, and let other people clean up the mess they had made. . . .