• Southwest is weighing changes to boarding and seating.
• The carrier stands out from other large airlines with its open seating plan.
• Meanwhile rivals like Delta and United have touted high revenue growth for premium seating.

Southwest Airlines is weighing changes to its cabin that could involve abandoning its single-class, open-seating system to drive up revenue, CEO Bob Jordan told CNBC on Thursday.

The changes would mark a massive shift for the carrier that has stood apart from rivals for decades with its simpler business model.

"We're looking into new initiatives, things like the way we seat and board our aircraft," Jordan said in an interview after the carrier's disappointing first-quarter report.

Southwest's all-Boeing 737 fleet has a single economy class cabin and no seating assignments, though it does offer earlier boarding to customers for a fee so they can snag their preferred seats. The airline has focused on keeping its product simple and user-friendly for years, aiming to keep its own costs and complexity to a minimum.

Meanwhile, rivals including Delta and United have touted high revenue growth for premium seating such as business class and strong upsell rates.

Jordan said no decisions have been made on what kind of changes Southwest will ultimately make, but he said studies have yielded "interesting" results.

"Customer preferences do change over time," Jordan said.

— CNBC's Phil LeBeau contributed to this report.