Activist investor Elliott Investment Management and Southwest Airlines are in talks to settle their months-long battle, according to reports Sunday, with a potential deal that would give Elliott representation on the budget airline’s board.

Elliott Investment Management and Southwest Airlines have begun discussing a potential settlement that would avoid a proxy fight for control of the airline's board, Bloomberg News reported on Saturday,

Elliott Investment Management and Southwest Airlines Co. have begun discussing a potential settlement that would avoid a proxy fight for control of the airline’s board, according to people familiar with the matter.