But both Burton and the company's chief executive deny the claim.
The Sunday Times story said Burton has received the plum assignment, then quotes her and McQueen CEO Jonathan Akeroyd saying this is not the case. Both flatly denied the McQueen house is involved.
The paper did not name any sources, suggesting the information had reached the newspaper after Akeroyd told a colleague about receiving the royal gig.
A Paris-based publicist for the McQueen house dismissed the report in an e-mail to The Associated Press, saying "We can confirm this story is untrue."
The contradictory story, which buzzed throughout Facebook and Twitter, did not clarify one of the central mysteries surrounding the April 29 wedding of Middleton and Prince William: Who will actually design the gown she wears for her transformation from commoner to princess?
The emphatic denials from the top people at McQueen would seem to indicate that the story is not true, but the circumstances surrounding the fashion assignment of the year (or perhaps the decade) make the situation somewhat cloudy.
Just two weeks ago, British Fashion Council chief executive Caroline Rush told The Associated Press that whoever had been chosen would be bound by the terms of the agreement to do everything possible to keep their role secret until Middleton walks down the aisle before the eyes of 1,900 invited guests and a vast global television audience.
"Whoever has the honor will be sure not to leak it, that's the agreement," she said as London Fashion Week closed without the identity of the designer being made public.
If word of the assignment has in fact leaked out, the designer would be in the awkward position of either breaking the terms of his or her contract by confirming their role or misleading the media and denying it in an effort to squelch the story.
As a result, the company's denial does not necessarily mean the McQueen house has not been chosen, fashion experts said Sunday, although some view the McQueen house as an unlikely winner, in part because of the publicity surrounding McQueen's suicide early last year.
The designer, seen by many as the most bold and original British designer of his generation, took his own life shortly after his mother's death. Burton, 36, who had worked closely with him for years, was named to the top creative position at the firm, and has been hailed for the skill and imagination she has brought to the difficult task of replacing a cherished, highly original talent.
American Vogue editor Anna Wintour called Burton "a brilliant choice" for the top job at McQueen during a visit to London Fashion Week in late February. The editor declined, however, to speculate about Middleton's choice for the wedding gown.
Burton is British, which would satisfy those hoping Middleton will choose a British designer, and under her leadership McQueen has maintained its reputation for dramatic design and phenomenal craftsmanship.
Still, many other accomplished designers remain in the running for the dream job, including Bruce Oldfield, Philippa Lepley, Daniela Issa Helayel and others. Issa has been favored by Middleton in the past, but is thought to be an unlikely choice because of her Brazilian roots and her relative inexperience with wedding gowns.
Prominent designers Vivienne Westwood and Christopher Bailey of Burberry Prorsum said during London Fashion Week that they had not received the coveted assignment.
Press aides handling the wedding for Prince Charles, Prince William's father, have repeatedly declined to comment on the dress. They point out the wedding is not a state affair and say Middleton deserves the right to surprise her husband with the gown.
Palace officials Sunday refused to comment on the report.
