Mr Branson is set to make his pledge at an industry conference in Chicago organised by the US Department of Transportation, where he will be one of the main speakers.
Mr Branson has been looking for an opening into the US for years, but is raising the tempo of his drive following Virgin's recent launch of a low-cost Australian carrier.
"The Australians have opened their skies, so two weeks ago Virgin announced a new carrier in Australia," Virgin said. "In the US, the law prevents us from doing so. This is the last big English-speaking market for us. "
Senator John McCain of Arizona, campaigning for the Republican Party's presidential nomination, is understood to have given his backing for Mr Branson's move.
Under current regulations, non-US companies are prohibited from owning majority stakes in US domestic carriers. US Government employees are also required to travel on US-owned carriers.
If Washington and London officials can conclude an agreement, Virgin will push to challenge Southwest Airlines, regarded as the country's leading domestic carrier.
Mr Branson said at the weekend that he would look to float the Australian operation in three to four years.
"We're going to have 300 Australian staff working for the airline, and at some time it would be good to share it with the Australian public," Mr Branson told an Australian television programme.
The venture, news of which sent the shares of Qantas and Ansett Australia sharply lower, is set to start operations in July and be in the black within three years, Mr Branson said.
Virgin Atlantic also said yesterday that the airline had been approached by the major aviation alliances following British Midland's recent move to join the Star Alliance. No deal is imminent, it said.
Mr Branson was quoted as saying: "If governments are going to allow alliances, then we are not going to be kept out in the cold.
"But we think that we will be able to come up with a deal that benefits our customers."