But the Atlanta-based carrier did not rule out the possibility of a merger with another airline.
"There have been no talks with United regarding any type of consolidation transaction and there are no such ongoing discussions," Delta's chief executive, Richard Anderson, said in a statement to The Times.
The Associated Press report, quoting an unnamed executive, said two carriers had talked as recently as a week ago about a possibility of a merger and that there was a "sense of urgency" to the talks.
It described how in one scenario, the combined carrier would keep the United name and be headquartered in Chicago, with Delta's Anderson as the CEO of the merged company.
United is the largest carrier at Los Angeles International Airport. Delta, the third-largest, has been recently beefing up flights at the airport.
"We do not respond to wholly inaccurate statements made by people who claim to have knowledge when they clearly do not," said Jean Medina, a United spokeswoman.
Earlier today, Delta had issued a statement saying that it had formed a special committee to "review and analyze strategic options."
It was in response to a letter it had received from a hedge fund that owns 7 million Delta shares. The fund, Pardus Capital Management, urged Delta to consider a merger with another airline in light of soaring fuel prices.
"We appreciate receiving Pardus' views on the best course for Delta's future," Anderson said, adding that the airline "believes that the right consolidation transaction could generate significant value for our shareholders and employees.
"With oil at over $90 a barrel, this analysis takes on a heightened importance as we factor those prices into our long-term planning process."