Anglo, which owns 45 per cent of De Beers, is considering making an offer for the 40 per cent stake held by the Oppenheimer family of South Africa, worth at least £2bn. The government of Botswana owns the rest.
Anglo is facing pressure from major investors to simplify its diamond interest by making De Beers part of the core group.
Alongside Anglo’s interest in diamonds through De Beers, the London and South Africa-listed group has mining operations in platinum, iron ore, copper, nickel and coal.
An Anglo spokesman said: “We’re not going to comment on speculation.”
The move to take control of De Beers from the Oppenheimers would cut established links between Anglo, the diamond firm and the family.
The Oppenheimers founded Anglo in 1917 and took control of De Beers in 1927, but Anglo later became a listed company. Anglo’s brokers are Swiss bank UBS and Goldman Sachs.
Last week, the Oppenheimers sold 2.1m shares in Anglo American.
In May, the owners of De Beers mulled re-listing the group after it went private in 2001, but De Beers dampened the talk in July, when it said its shareholders were not working on a re-listing.