CHICAGO (Reuters) - Activist investor Elliott Investment Management told one of Southwest Airlines' top unions it still wants to replace CEO Robert Jordan, according to a union memo seen by Reuters, even after the carrier pledged to shake up its board.

Elliott, which owns 10% of Southwest's common shares, met with the Aircraft Mechanics Fraternal Association on Sept. 12, the memo to members said. The union represents about 3,000 mechanics at the Dallas-based airline.

"Its vision of a Southwest turnaround is one where Robert Jordan does not remain as CEO," the memo said. The union also said the hedge fund wants Gary Kelly, who is executive chairman, to leave sooner than his planned departure date.

The meeting took place two days after Southwest said six directors would step down in November and Kelly would retire next year, but that it remained committed to Jordan. The board revamp was announced after the carrier and hedge fund met last week.

The hedge fund now owns enough Southwest stock to call a special meeting and take the next steps to shake up the board and management. In August, Elliott identified 10 director candidates it could nominate to the 15-member board.

Other Southwest investors have met with Elliott and some of the hedge fund's director candidates in the last few days. At these meetings, the hedge fund underscored its desire to replace Jordan and get an earlier departure for Kelly, an investor familiar with the meetings said. Jordan succeeded Kelly as CEO in 2022.

Elliott has pushed hard for the replacement of Jordan and Kelly, blaming them for the airline's struggles. It wants the carrier to be more competitive in the industry and has been holding meetings with unions to boost support for its campaign. 

In the meeting with the mechanics union, the hedge fund insisted that Jordan be replaced, the memo said. It also advocated the departure of other top executives, it added.

Elliott declined to comment. Last week, it called the planned board changes "unprecedented" and praised the board for "beginning to recognize the degree of change that will be required at Southwest."

Southwest did not immediately respond to a request for comments.

The airline last week said it would appoint four new independent directors in the near future and would potentially include up to three candidates proposed by Elliott.

However, the company expressed confidence in Jordan, saying there was "no better leader" to successfully execute its strategy to "evolve the airline and enhance sustainable shareholder value."

Southwest has been struggling to find its footing after the pandemic, in part due to Boeing's aircraft delivery delays and industrywide overcapacity in the domestic market.

It plans to offer assigned and extra-legroom seats to attract premium travelers, and start overnight flights. It will present details to investors on Sept. 26.

The mechanics union said Elliott noted the proposed board overhaul was not part of a negotiated deal but rather announced by the airline and presented to the hedge fund.

Jordan told staff last week that the Sept. 9 meeting with the hedge fund was "productive." He said the company looked forward to continuing to work with Elliott toward a "collaborative resolution" in the near future. 

"Southwest has a great plan," Jordan said, adding the board and corporate governance changes would help the company return to "the high level of financial performance that we - and our shareholders - expect."

The mechanics union said Elliott has hired consulting firm Gephardt Group to investigate Southwest's recent approach to labor relations.

Southwest has also been trying to rally its workers and investors.