Elliott Investment Management and Southwest Airlines (NYSE:LUV) have begun discussing a potential settlement that could avoid a proxy fight for control of the airline company’s board. What Happened: Elliott has proposed a plan that involves giving it representation on the airline’s board without control, Bloomberg reported on Saturday, citing people familiar with the matter. The report added that the talks are progressing towards a resolution. However, they haven’t been finalized and could also be unsuccessful, it said. Benzinga has reached out to both Southwest and Elliott for confirmation bu…