BP's chief executive Tony Hayward has been negotiating the terms of his exit, with a formal announcement likely within 24 hours, the BBC has learned.
Mr Hayward has been widely criticised over the Gulf of Mexico oil spill.
An official statement issued by BP in response said he had the "full support of the board and senior management".
BBC business editor Robert Peston says Mr Hayward is likely to be replaced by his American colleague, Bob Dudley, who is in charge of the clean-up operation.
While BP has been preparing for a change at the top for some time, the company was waiting until progress had been made on stemming the leak and until it was possible to quantify the financial costs of the disaster, our correspondent adds.
BP is due to release its results for the second quarter on Tuesday. It is expected to reveal a provision of up to $30bn (£19bn) for the costs of the clean-up, compensation claims and fines to be paid, resulting in a massive quarterly loss. It has also lost 40% of its market capitalisation.
BP's board is scheduled to meet on Monday ahead of the results, when it is expected to discuss the timing of Mr Hayward's exit.
The official overseeing the US government response to the oil spill has meanwhile said the operation to plug the ruptured Macondo well permanently has been put back to allow more time for preparatory work.
Retired Coast Guard admiral Thad Allen said the last bit of pipe needed for the process would be put in place in the coming this week, with the actual plugging operation starting in the first week of August.
A temporary cap has stopped oil from gushing for more than a week.
Mr Hayward has been with BP for 28 years. When he became chief executive in 2007, he told journalists his number-one task was to focus "laser-like" on safety and reliability.
But the explosion on the drilling rig off Louisiana on 20 April, which killed 11 workers and triggered the worst oil spill in US history, has raised questions about his leadership.
The 53-year-old has been heavily criticised by residents of the Gulf coast and US politicians for his handling of the clean-up operation and for a series of gaffes, including saying that he "just wanted his life back" and that the Gulf is a "big ocean" following the leak.
He was also taken to task for attending a sailing event off the Isle of Wight in June.
Mr Hayward was also publicly rebuked by members of the House Energy and Commerce Committee last month for "stonewalling" questions at a congressional hearing and of "kicking the can down the road".
Responding to reports that Mr Hayward was expected to step down, US Congressman Ed Markey - who chairs a committee covering the oil spill issue - said: "While it's now happy sailing for Tony Hayward, rough conditions will persist in the Gulf of Mexico for years to come because of his failed leadership.
"The new leaders of BP will have an uphill climb to correct the legacy [he] left," he added.
The man expected to replace Mr Hayward, BP Managing Director Bob Dudley, took over the day-to-day operations in the Gulf last month.
Many say that, from a public relations point of view, Mr Dudley has the advantage of being American and speaking with an American accent. He grew up in Mississippi and, according to BP, has a "deep appreciation and affinity for the Gulf Coast".
Mr Dudley joined BP in 1999 following a merger with Amoco and rose to the board last year.
He is probably best-known for running BP's joint venture in Russia, TNK-BP, during the public falling-out with its Russian partners.
Dr Richard Pike, chief executive of the Royal Society of Chemistry, said that perception was the key reason behind the change.
"If your major shareholders are getting the impression that there is a major problem here then that is key over and above anything the chief executive or his board of directors has done," he told the BBC.
"In many ways changing the chief executive is as much practical as it is symbolic; it all rests on reputation."