BP is in exclusive talks to sell up to $12 billion (£8 billion) of assets to Apache Corporation, an American rival, including a big stake in Alaska’s Prudhoe Bay, the largest oil field in North America, it was reported Sunday.

Apache approached BP with the plan a few weeks ago. Negotiations are under way over the structure of the agreement and what other assets could be included.

The British oil giant has been trying to sell assets as part of a huge fundraising campaign to meet the costs of its disastrous oil spill in the Gulf of Mexico.

This weekend the company is trying to install a tighter seal over the leaking well, which has been pouring oil since a blowout in April. A relief well that may close it off could be complete before the end of the month.

Good news from the gulf could tempt rivals to examine a bid for BP while its share price is still depressed.

Oil industry sources said that Exxon, the world’s largest oil company, has been given a green light by the American government to “take a look”. “They have been told there is no problem in principle,” the source said.

A spokesman for Exxon declined to comment, and the sources said it was far from certain that Exxon would make a move. A merger would create a group with a stock-market value of $400 billion.

If the Apache talks are successful, the deal could at a stroke meet BP’s targets for raising cash from asset disposals. It said it wanted to raise $10 billion from disposals, and billions more from bond issues and bank loans. It is unclear what other assets would be included in an any transaction.

The cash will help to reassure investors that the cost of the clean-up will not overwhelm the company. Goldman Sachs, the American investment bank, thinks BP could ultimately be forced to pay $70 billion in clean-up and compensation costs.

The Apache talks are just one of three separate sales processes BP has launched.

The second involves its $9 billion stake in Pan American Energy, an Argentinian oil producer. CNOOC, the Chinese oil group, and Bridas, a rival Argentinian firm, are considering buying part or all of BP’s 60 percent holding.

The third leg is the auction of several asset packages, including its businesses in Venezuela and Colombia, together worth about $1 billion, and in Vietnam, which could fetch a similar amount.

Apache, worth $29 billion, is one of America’s largest independent oil groups. It has a history of doing similar smaller deals with BP. In 2003 it paid $1.3 billion for the giant Forties field in the North Sea. Three years later it struck a deal for 18 BP fields in the Gulf of Mexico.