Lehman Brothers Holdings Inc., the investment bank that’s trying to shed mortgage assets and raise capital, is poised to eliminate as many as 1,000 jobs, or about 4% of its workforce, in the fourth round of cuts at the firm this year, people familiar with the matter said.

The headcount reductions may be announced when Lehman, the fourth-largest American securities firm, reports third-quarter financial results next month, according to the people, who declined to be identified because the plan isn’t completed.

Lehman, based in New York, has shrunk its payroll by about 6,400, or 22%, in the past 12 months as its share price sank 70%. Banks and securities firms have eliminated 101,250 jobs as credit losses and writedowns stemming from the collapse of the subprime mortgage market last year have exceeded $512 billion.

“The sharp decline in its stock price and what I believe is the real likelihood of a hostile takeover may now be forcing management to deal with its problems,” an analyst at Ladenburg Thalmann & Co. in Lutz, Florida, Richard Bove, said in a report today.

A Lehman spokesman, Brian Finnegan, declined to comment.

The chief executive officer, Richard Fuld, 62, is seeking to dispose of hard-to-sell assets connected to the American housing market after posting a $2.8 billion loss in the previous quarter because of writedowns on the investments.

Lehman, the No. 1 underwriter of mortgage-backed securities last year, was saddled with the stakes after investor demand for them dried up.

The first round of job cuts started last year at the firm’s mortgage units, which originated the loans to homeowners. The loans were then packaged into bonds to be sold to investors.

The New York Times, citing a person briefed on the firm’s plan, reported yesterday that Lehman plans to eliminate as many as 1,500 jobs in the pending round of cuts.

Lehman rose $1.09, or 7.4%, to $15.87 at 4:11 p.m. in New York Stock Exchange composite trading.