Buffett's company Berkshire Hathaway has stakes in Delta, American, United and Southwest. "I wouldn't rule out owning an entire airline," Buffett said on CNBC in late February. Atlanta-based Delta is the largest carrier at Hartsfield-Jackson International, while Southwest is the second-largest.

According to Wolfe Research senior analyst Hunter Keay in a Friday note to investors, most analysts appear to be focusing on Southwest and Delta "as the most likely two candidates, which seem like logical choices due to cash flow, balance sheet, brand reputation, and general overall quality." Keay wrote that Southwest "has the characteristics of a typical" Berkshire Hathaway acquisition candidate, but noted that Berkshire took interest in a presentation by American Airlines CEO Doug Parker, according to media reports.