David Solomon was fed up with his critics inside Goldman Sachs GS -1.18%decrease; red down pointing triangle. The time had come to crack down.

It was bad enough that Goldman partners were criticizing the chief executive’s leadership and bad-mouthing the storied bank’s costly expansion of consumer lending. What rankled Solomon even more was the suspicion that some of the naysayers were leaking details to reporters. Goldman launched a probe to figure out who was talking, according to people familiar with the probe.