NEW YORK — The investment bank Morgan Stanley plans to cut about 1,600 jobs, nearly 3 percent of its workforce, a person familiar with the bank said Wednesday. The cuts will focus on senior ranks at the bank.

About half of the cuts will be in the United States. Morgan Stanley’s investment banking unit has been asked to cut about 6 percent of its staff. Back-office functions, including human resources and communications, have also been asked to cut staff. The person familiar with the matter wasn’t authorized to speak on the record and insisted on remaining anonymous.