The cuts will mostly be in back-office jobs, which entail processing trades, since it trimmed front-office traders and bankers last year, the source said, adding that none of the cuts will come from the bank's network of financial advisers.
Morgan Stanley declined to comment.
The company had a total of 46,964 employees at the end of November, according to a filing with the US Securities and Exchange Commission.
The bank slashed non-broker jobs in several rounds last year as Chief Executive John Mack tried to better equip Morgan Stanley for a period of lower revenue.
Broker jobs have been saved because the wealth management business has been a bright spot for the company.
Earlier this month, Citigroup Inc agreed to merge its Smith Barney brokerage with Morgan Stanley's wealth business.
The deepening global recession has triggered more losses for Morgan Stanley's investment bank, and in December the company reported a wider-than-expected quarterly loss of $2.2 billion (Dh8 billion).
Shares in Morgan Stanley rose 1.2 per cent at $20.48 in afternoon trading. The company's shares have climbed more than 25 per cent since the start of the year.
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