(Reuters) -Elliott Investment Management and Southwest Airlines ( LUV ) have begun discussing a potential settlement that would avoid a proxy fight for control of the airline's board, Bloomberg News reported on Saturday, citing people familiar with the matter.

Elliott has proposed a framework that would give it representation on Southwest's ( LUV ) board but not control, the people said, adding that the talks, which were progressing toward a resolution as of Saturday, have not been finalized and could fall through.

Southwest ( LUV ) and Elliott did not immediately respond to a Reuters' request for comment.

On Monday, the hedge fund officially called for the special meeting to be held on Dec. 10 and submitted proposals to replace eight directors and take control of the board.

The company said it tried to reach a resolution to avoid a fight and noted that the timing of the proposed special meeting was designed to "maximize disruption" before one of the busiest travel periods of the year.

The activist investor which owns 10% of Southwest's ( LUV ) common stock, has pushed for months to replace some members of the board, oust CEO Bob Jordan, and review its strategy to improve financial performance and boost the share price.

The airline unveiled several initiatives last month to shore up sagging profits, including partnerships, vacation packages for customers and aircraft sale-leasebacks.

As one of the biggest and busiest activist investors, Elliott has previously pushed for changes at coffee chain Starbucks, Salesforce and Twitter.