Southwest Airlines and Elliott Management are near a settlement which will stave off a proxy fight at the carrier, a person familiar with the matter said. The deal will give Elliott a sizable representation on the company's board but would fall short of a majority.

Elliott Investment Management and Southwest Airlines Co. are nearing a settlement that would avoid a proxy fight for control of the carrier’s board, according to people familiar with the matter.

The parties are currently negotiating terms that would provide Elliott with a number of board seats, though less than the majority, to ensure that control remains with the airline, according to a report.