The planned card would carry the Apple Pay brand and could launch early next year, the Journal reported, citing people familiar with the matter.
The iPhone maker will replace its longstanding rewards-card partnership with Barclays (BARC.L), the report added.
Goldman Sachs, Apple and Barclays all declined comment.
The news comes as Apple sharpens its focus on its services business that includes the App Store, mobile payments and music streaming. The unit’s revenue grew 31 percent to more than $9 billion (6.7 billion pounds) in the three months ended March 31.
Goldman has been looking to expand its consumer banking business to offset weakness at its trading unit. Last year, the Wall Street bank’s executives laid out a goal to generate $5 billion in revenue from new sources, including consumer banking.
In February, the Wall Street Journal reported that Apple was in talks with Goldman to offer financing to shoppers buying Apple products, including iPhones.
Reporting By Aparajita Saxena in Bengaluru; Editing by Sai Sachin Ravikumar