The talks are understood to be at a fairly advanced stage, although there is no certainty they will result in agreement.
However, analysts said there would be strong commercial logic to a tie- up between the two. A merger of BP Amoco and Atlantic Richfield (Arco) would create a group with sales approaching $80bn, reserves of more than 13 billion barrels of oil and a market capitalisation of about $185bn, putting it ahead of Royal Dutch Shell but still behind Exxon-Mobil.
BP Amoco, itself the result of an pounds 80bn merger last year, and Arco are joint operators of the biggest oil field in North America - the Prudhoe Bay field in Alaska.
There has long been speculation that they might merge their activities to cut costs, particularly in light of low oil prices. Although the price of crude has risen from $10 to $14 a barrel in the past two months, it remains low by historic standards.
If BP Amoco is to pull off another acquisition so soon after last year's Amoco takeover, analysts believe now might be the time to strike before the oil price rally starts to be reflected in company valuations.
Apart from Alaska, Arco has extensive petrol retailing interests and some refining capacity on the West Coast of America, where BP Amoco has relatively little presence. It also has reserves in the Far East and Middle East, which would help make it a good strategic fit for BP Amoco.
Last year, Los Angeles- based Atlantic Richfield had revenues of $10.3bn. It made a fourth-quarter loss of nearly $800m after taking heavy charges to cover 1,200 job cuts and a writedown in the value of some of its oil and gas fields following the decline in oil prices. It was the company's first quarterly loss in six years, and it left Atlantic Richfield with a loss for the year of $631m.
In October last year the Atlantic Richfield chief executive, Michael Bowlin, pledged that the company would stay independent despite the fall in oil prices, and announced an efficiency programme aimed at saving $500m a year by 2000.
A BP Amoco spokesman said: "We do not comment on market rumours."
Meanwhile, BP Amoco is also continuing talks with Mobil to buy out its minority share in their European petrol retailing joint venture. The European Commission has told Mobil it must dispose of its 30 per cent share of the joint venture following its takeover by Exxon. The deal could cost BP Amoco $2bn. It has a 70 per cent stake in the venture, which operates a chain of more than 5,000 petrol stations throughout Europe.
But BP Amoco is in a strong position, with cost savings from the merger flowing through faster than originally forecast.
Sir John Browne, the BP Amoco chief executive, said last month that he expected to achieve $2bn of savings by February 2000, a year ahead of schedule. Most analysts believe the eventual savings will be nearer to $3bn.