The remaining 51 percent of Virgin Atlantic is owned by billionaire Richard Branson, who founded the airline in 1984.
Singapore has been considering selling its stake in Virgin for several years and has talked with Delta about a sale in the past, according to the Wall Street Journal.
Virgin has been looking for a possible suitor, too. It hired investment firm Deutsche Bank in 2010 to explore its options.
Buying Virgin is attractive to a carrier like Delta because of its potential to unlock more access to London's Heathrow airport, a key international gateway. Virgin is the second-biggest airline there after British Airways.