The two sides have been discussing a potential settlement that would avoid a proxy fight for control of the airline’s board, people familiar with the matter said Saturday. Elliott has proposed a framework that would give it representation but not control of the board, said some of the people, who asked to not be identified because the discussions aren’t public. 

New York-based Elliott disclosed an initial stake of roughly $2 billion in Southwest in June. It called for strategy and leadership changes at the carrier after what it saw as years of underperformance, pointing the finger squarely at Chief Executive Officer Bob Jordan and Chairman Gary Kelly.

Kelly has since said he’ll step down along with half a dozen directors. But the airline has thrown its support behind Jordan, whom Elliott has been seeking to force out. The activist has accused the leaders of refusing to upgrade operations, hurting shareholders and leaving Southwest unable to withstand competitive challenges.

The talks, which were progressing toward a resolution as of Saturday, haven’t been finalized and could fall through, the people said. Representatives for Southwest and Elliott declined to comment. 

The airline has announced major policy changes as part of plans to revitalize operations and fend off Elliott. For example, Southwest will begin selling assigned seats late next year and introduce a premium fare option offering extra leg room.

The changes break from tenets that helped set Southwest apart for decades, after the carrier was slow to embrace the industry’s push to capture growing demand for premium flying options. The Dallas-based carrier has said it will retain its policy of two free checked bags.

Elliott has nominated eight directors to the Southwest board and called for a special shareholder meeting on Dec. 10, setting up what would be the firm’s first US proxy fight since 2017. An actual date for a meeting hasn’t been set.

In response, Southwest said its board had made every effort to reach a constructive resolution with Elliott, including providing a settlement framework for appointing as many as three of the activist’s nominees. It said Elliott’s special-meeting request was unnecessary and inappropriate.

The airline also unveiled a $2.5 billion stock buyback plan last month. Other steps have included adopting a poison pill shareholder rights plan and naming two veteran airline executives to its board. The carrier will also create a new finance committee to oversee financial, operational and business plans and strategies going forward.

Southwest shares have advanced about 7% so far this year. While that’s less than the 10% increase of the 30-member Bloomberg World Airlines Index, it puts the stock on course for its first annual gain since 2019.