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BP chief Tony Hayward 'negotiating exit deal'
Mr Hayward has been widely criticised over the Gulf of Mexico oil spill.
BBC business editor Robert Peston said it was likely he would be replaced by his US colleague Bob Dudley, now in charge of the clean-up operation.
BP said Mr Hayward "remains our chief executive and has the full support of the board and senior management".
Our correspondent added that while BP had 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.
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 capping the well, compensation claims and fines to be paid, resulting in a massive quarterly loss.
BP's board is scheduled to meet on Monday ahead of the results.
Mr Hayward has been with the company for 28 years.
He has also been rapped by US congressmen for not taking responsibility for the disaster at its Macondo oil well, which killed 11 people.
The congressmen were unimpressed by the answers they received from the BP boss at a congressional committee on energy and commerce hearing last month.
They accused him of "stonewalling" questions and of "kicking the can [of responsibility] down the road".
Mr Hayward had already been lambasted for 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 in June by those, including the White House, who felt he should have been dealing with the leak.
Bob Dudley Many commentators believe Mr Dudley's American accent will be advantageous from a PR perspective
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.
"The only way BP can be considered anew is if its leadership team does everything it can to renew the Gulf and bring about a new era of safe oil exploration, governed by transparency and accountability."
Reputation is key
The man expected to replace Mr Hayward, Bob Dudley, took over the day-to-day operations in the Gulf of Mexico 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 US oil firm Amoco.
He is probably best-known for running BP's joint venture in Russia, TNK-BP, during the public falling-out with its Russian partners.
He joined the BP board in April 2009.
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.
"BP hopes the next few days will be the start of a new beginning for the company," he added.