The move comes as Apple puts increasing focus on revenue from online services and content, and as Goldman Sachs seeks to make more money from consumer banking operations.
Apple declined to comment on the report, which cited unnamed people close to the matter.
A joint credit card bearing the Apple Pay brand could launch early next year, and replace a rewards-card partnership Apple has with Barclays, according to the Journal.
Apple, which still gets most revenue from the iPhone, reported a hefty rise in earnings during the first three months of this year, alleviating worries about the iPhone's prospects and a hit from US-China trade tensions.
Analysts praised a big jump in revenues in Apple's services business, which is seen as an important element of diversification away from having revenues tied to gadgets.
A 31 percent rise in services to $9.2 billion (roughly Rs. 60,400 crores) was credited to revenue gains from Apple Pay, Apple Music and other programs.
Goldman Sachs Bank USA last month acquired personal finance startup Clarity Money. Financial terms of the deal were not disclosed.
Free-to-use Clarity Money is a leading app that uses artificial intelligence to help people manage their finances with personalised, "actionable insights" such as saving money or finding better credit cards, according to Goldman Sachs.
"Consumers want a better way to manage their finances," GS Bank chief executive Stephen Scherr said in a release.