The job cuts will largely affect technology and operations positions at the investment bank, CNBC reported, citing people with knowledge of the situation.
Morgan Stanley had just more than 60,000 employees at the time of its last quarterly report to the Securities and Exchange Commission on Sept. 30.
Financial firms on Wall Street frequently eliminate jobs near the end of the year to escape having to pay bonuses, the report noted.
A representative of Morgan Stanley said the company had no comment on the report.
Shares of Morgan Stanley fell 20 cents or 0.4%, to end the day at $49.60. The shares have risen about 25% so far this year.
Financial stocks were generally lower Monday.
The S&P 500 financial sector index fell 1.16, or 0.23%, to 501.42.