The

GE

GE 0.29%

unit, known as GE Capital Aviation Services, or Gecas, is the biggest remaining piece of GE Capital, a once-sprawling lending operation that rivaled the biggest U.S. banks but nearly sank the company during the 2008 financial crisis. GE already took a major step back from the lending business in 2015 when it said it would exit the bulk of GE Capital, and a deal for Gecas would represent another big move in that direction.

It would also represent another significant move by GE Chief Executive Larry Culp to right the course of a company that has been battered in recent years by souring prospects for some of its top business lines and a structure that has fallen out of favor with investors.

With more than 1,600 aircraft owned or on order, Gecas is one of the world’s biggest jet-leasing companies, alongside AerCap and Los Angeles-based Air Lease Corp. It leases passenger aircraft made by Boeing Co. and

Airbus SE

as well as regional jets and cargo planes to customers ranging from flagship airlines to startups. Gecas had $35.86 billion in assets as of Dec. 31.

AerCap has a market value of $6.5 billion and an enterprise value—adjusted for debt and cash—of about $34 billion, according to S&P Capital IQ, and around 1,400 owned or ordered aircraft. The company has experience in deal making, paying around $7.6 billion in 2014 to buy International Lease Finance Corp. AerCap’s revenue last year was about $4.4 billion, down from around $5 billion in the previous few years.

The aviation business has been hit hard by the Covid-19 pandemic, which has resulted in a sharp drop in global travel and prompted airlines to ground planes. Some airlines have sought to defer lease payments or purchases of new aircraft. Gecas had an operating loss of $786 million on revenue of $3.95 billion in 2020. GE took a roughly $500 million write-down on the value of its aircraft portfolio in the fourth quarter.

Combining the companies could afford cost-cutting opportunities and help the new entity weather the downturn.

Separating Gecas could help GE with its efforts to shore up its balance sheet and improve cash flows. Despite a recent increase, GE’s share price remains below where it was before significant problems in the company’s power and finance units emerged in recent years.

The Boston company has a market value of around $119 billion after the shares more than doubled in the past six months as it posted improving results. Still, the stock has fallen by about three-quarters from the peak just over 20 years ago.

Mr. Culp became the first CEO from outside of GE in late 2018 after the company was forced to slash its dividend and sell off businesses. The former

Danaher Corp.

boss has sought to simplify GE’s wide-ranging conglomerate structure further, as other industrial giants such as Siemens AG and

Honeywell International Inc.

have done in recent years.

Activist investor Trian Fund Management LP, which has owned a significant position in the company since 2015 and holds a seat on its board, has supported such changes.

Early in his tenure, Mr. Culp said he had no plans to sell Gecas, a move his predecessor

John Flannery

had considered after the unit drew interest from private-equity firms pushing further into the leasing business.

Mr. Culp has sought to even out cash flows and refocus on core areas. Operations he has parted with include the company’s biotech business, which was purchased by Danaher in a $21 billion deal that closed last year. GE also sold its iconic lightbulb business in a much smaller deal last year, and previously said it was unloading its majority stake in oil-field-services firm Baker Hughes Co.

GE has cut overhead costs and jobs in its jet-engine unit while streamlining its power business. The pandemic continues to pressure the jet-engine business, GE’s largest division, however.

The company also makes healthcare machines and power-generating equipment, and the rest of GE Capital extends loans to help customers purchase its machines and contains legacy insurance assets too.

AerCap is based in Ireland and Gecas has headquarters there as well. The aircraft-leasing industry has long had a significant presence in Ireland due to the country’s favorable tax regime and the importance of Guinness Peat Aviation in the development of the sector. (A deal between GE and AerCap would reunite two companies that bought their main assets from GPA.) The industry has gotten more competitive as Chinese companies have gained market share, however, and the combination could help the new group stem that tide.

Shares in aircraft-leasing companies plummeted along with much of the market in the early days of the pandemic as demand from major airlines, who lease planes to avoid the costs of owning them, evaporated. But many of the major lessors’ stocks have recovered lost ground and then some in the months since as lockdowns ease and the outlook for travel improves.

AerCap’s Chief Executive Aengus Kelly said on its fourth-quarter earnings call this month that he expects airlines to shift more toward leasing planes as they rebuild their balance sheets, in what would be a boon to the company and its peers.

“Their appetite for deploying large amounts of scarce capital to aircraft purchases will remain muted for some time,” he said. “The priority will be to repay debt or government subsidies.”

—Thomas Gryta contributed to this article.

Write to Cara Lombardo at cara.lombardo@wsj.com and Emily Glazer at emily.glazer@wsj.com