Hayward is set to take a post at TNK-BP, the company's joint venture in Russia, according to the person, who spoke on condition of anonymity because an official announcement had not been made by the British company's board.
The move was being made more than three months after an oil rig explosion set off the spill and less than two weeks after a temporary cap finally stopped the oil from leaking. The government's oil spill chief, retired Coast Guard Adm. Thad Allen, said in Washington on Monday that efforts to solidly seal BP's busted deep-sea well are set to begin in a week.
Moving Hayward gives BP a chance to make a fresh start. BP executive Robert Dudley, an American who has been overseeing oil spill recovery efforts, is likely to be his successor.
"The sooner Bob Dudley is empowered to act as CEO, especially with regard to the U.S., the better it will prove to be for BP," said Stephen Pope, the chief global equity strategist at Cantor Fitzgerald in London.
The board met Monday but it was unclear whether it had made the demotion official. A statement was expected early today, at the same time the company files its second quarter results.
Hayward left BP's headquarters after the board meeting without speaking to reporters. The Briton's silver Lexus was mobbed by photographers, who chased the car down the tony street in central London.
It's not yet clear what Hayward's role will be with TNK-BP, but the job suggests BP still holds more faith in Hayward than much of the U.S. public and political establishment do. Analysts consider the Russian venture one of BP's crown jewels; it accounts for a quarter of the company's production.
TNK-BP's challenges are well known to Hayward's likely successor as CEO, who used to run it. Dudley was forced to flee Russia in 2008 and ran BP's interests there in absentia until that became untenable after a dispute with Russian shareholders.
Repeated calls to TNK-BP's offices in Moscow went unanswered Monday.
BP owns half of the oil firm, which is Russia's third-largest. Moving Hayward gives insiders who believed he was scapegoated for his off-the-cuff remarks a chance to keep a highly trained professional in the company.
"They still think highly of Tony Hayward but they have to get him away from this situation," said Phil Weiss, an oil analyst with Argus Research in New York. "TNK-BP is an important part of BP."
Hayward was called back to London a month ago after a bruising encounter with a congressional committee and has since kept a low profile. There is persistent speculation that BP Chairman Karl-Henric Svanberg, who moved into the post on Jan. 1, is also likely to lose his job later this year.
In New York, BP shares rose almost 5 percent Monday as the stock market anticipated a formal announcement about Hayward. Shares of BP PLC rose $1.79, or 4.9 percent, to close at $38.65 Monday in New York. BP shares closed up 4.6 percent at 416.95 pence ($6.45) in London.
The one-day board meeting comes a day before BP announces earnings for the second quarter. That report is expected to include preliminary provisions for the cost of the Gulf disaster, which analysts say could be as high as $30 billion.
Hayward, 53, who has a doctorate in geology, had been a well-regarded chief executive. But his promise when he took the job in 2007 to focus on safety "like a laser" came back to haunt him after the April 20 explosion on the Deepwater Horizon rig, which killed 11 workers and unleashed a gusher of oil a mile below the surface.
His early attempts to shift blame to the rig owner, Transocean, failed to take the heat off BP. Later remarks that the amount of oil pouring into the Gulf was "tiny" compared to its volume of water and his complaint that he would "like my life back" made him an object of scorn.
Dudley assumed oversight of the oil spill recovery last month, soon after Hayward was pilloried for spending a day at a yacht race at the height of the disaster.
New Orleans Mayor Mitch Landrieu said BP's attitude about making things right was more important than who is running the company.
"BP, from I think everybody's perspective, made a very bad mistake," he said. "I think what the world expects from BP is an acknowledgment that something was done wrong. I think BP has a long way to go to gain the trust of the people."
Allen, the Obama administration's point man on the spill, indicated that Hayward's departure would not significantly affect the government's relationship with BP as it presses the company to plug the leak, clean up the mess and compensate people harmed by the spill.
"I talk to Bob Dudley when I need to. ... I woke him up on a number of occasions from time to time," Allen said. "The communication is frequent. It also was frequent when Tony Hayward occupied that position. There's no material difference in my level of communication with either one."
Allen said the so-called "static kill" -- in which mud and cement are pumped into the top of the well -- should start Aug. 2. Because the well is now capped, that effort will be more controlled than a previous failed effort, a "top kill" in which mud was shot into the still-spewing well.
A relief well is nearly complete for the final stage, a "bottom kill" in which mud and cement are pumped in from deep underground. Allen said that work could begin Aug. 7 and could take days or weeks, depending on how well the static kill works.
Delays are possible, though. Tropical storm forecasts last week forced crews to suspend their work about 50 miles off the Louisiana coast for several days. Allen says he'll order an evacuation again if a similar storm forms.
Weber contributed to this story from New Orleans; Associated Press Writers Robert Barr in London and Mansur Mirovalev in Moscow contributed to this story.