Bingham has advised Oculus VR, a maker of virtual-reality goggles, that Facebook agreed to acquire. Associated Press

Boston law firm Bingham McCutchen LLP is on the hunt for a merger partner, according to two people familiar with the matter.

The overtures follow a challenging year-and-a-half for the firm, which has about 850 lawyers in 14 offices world-wide. A number of partners have left, and last year Bingham's revenue slid by 12.6%.

In May the law firm announced that longtime chairman Jay Zimmerman would be handing over the reins to managing partner Steven Browne. Overtures to at least one rival firm began within the month, one person familiar with the matter said.

The firm declined to comment on any current merger talks, which were first reported by Reuters.

In a statement, a Bingham spokeswoman said the firm has "engaged in talks with scores of firms during the past 20 years, some of which we have acted upon, most of which we have not."

The firm is "always open to exploring opportunities," she said. "Our financial performance is very strong, and we are on track to have a much better year than we did in 2013," she added.

Bingham isn't alone in its difficulties. Big law firms have been grappling with a tough legal market since the financial crisis. Demand has rebounded somewhat as the economy improved, including a recent surge in high-end mergers and acquisitions work.

But competition for clients and the most profitable matters remains fierce across the legal world.

In recent years a number of law firms have decided to chase growth by teaming up with rivals. Law firm mergers can offer instant access to new markets, and the potential to boost profits for lawyers on both sides. But they can also be expensive, and risky.

The biggest merger so far this year was between Washington, D.C.'s Patton Boggs LLP and the larger international firm Squire Sanders, a union that produced Squire Patton Boggs, with more than 1,500 lawyers.

Whether wedding bells are in store for Bingham in the near future remains unclear. Many merger talks end up going nowhere, spiked by client conflicts, clashes over firm culture or concerns about a potential partner's financial health.

Bingham lawyers continue to work on high-profile matters. The firm has advised Amazon.com Inc. on tax issues, and has offered merger-and-acquisition guidance to Oculus VR Inc., a maker of virtual-reality goggles, that Facebook Inc. agreed to acquire in March for $2 billion.

Over the past month the firm has also brought in some new hires, including a team of life-sciences lawyers from Cooley LLP and mergers-and-acquisitions partner Fred Chang in Beijing. This week Bingham plans to announce that prosecutor David Miller, a former assistant U.S. attorney in the Southern District of New York, is joining the firm's white-collar investigations and enforcement group.

Still, the departures continue. On Monday, tax partner Matthew Schnall, who worked on the Oculus-Facebook deal, is joining the Boston office of Wilmer Cutler Pickering Hale and Dorr LLP, according to WilmerHale. Mr. Schnall spent the past two decades at Bingham, where he represented clients in tax controversies, transactional planning and other matters.

Write to Jennifer Smith at jennifer.smith@wsj.com