Deutsche Bank AG is weighing whether to cut 15,000 to 20,000 jobs, or more than one in six full-time positions globally, according to a person familiar with high-level discussions about the latest attempts to turn around the struggling financial giant.

The cuts being contemplated by senior executives reflect an acceleration of Deutsche Bank’s downsizing and another major pullback from its global ambitions. If followed through, the reduction would represent 16% to 22% of Deutsche Bank’s workforce of 91,463 employees, as disclosed...