Delta Air Lines Inc. is close to striking a deal to acquire a 49% stake in Virgin Atlantic Airways Ltd., a person with knowledge of the talks said, in a move that would boost the U.S. carrier's presence at London's congested Heathrow Airport and continue a run of cut-price deals to expand its network.

The No. 2 U.S. carrier by traffic is expected to acquire the stake from Singapore Airlines Ltd. for between $300 million and $500 million and retain the Virgin brand, according to the person with knowledge of the discussions....