Southwest Airlines shares surged more than 4 percent on Thursday after a rumor circulated on Twitter that billionaire investor Warren Buffett wants to acquire the remaining shares of the low-cost airline.

Buffett's Berkshire Hathaway is already Southwest's second-largest shareholder and had an 8.7 percent stake worth more than $2.2 billion, according to Berkshire's annual letter released last week. Berkshire Hathaway is also one of the largest shareholders in Southwest's competitors Delta Air Lines, United Airlines and American Airlines.

"$LUV talk Berkshire Hathaway seeking to acquire remaining shares of Southwest" at $75 a share, said a tweet from Twitter user StockTraders.net, a trading portal. It called the talk "unconfirmed." Southwest shares closed at $56.04 on Thursday.

Southwest acknowledged the rumor but declined to comment.