Bank of America Corp. is about to decide just how big it wants to be in payments.

Executives at the lender have only weeks left to tell First Data Corp. whether they want to wind down a decade-old joint venture scheduled to renew automatically in mid-2020, according to an April regulatory filing. Known as Bank of America Merchant Services, the unit helps retailers and other clients handle electronic payments. But Bank of America could offer those services directly, potentially strengthening...