The acquisition of about 9 per cent shares on top of 12.43 per cent bought in March will give Agarwal an indirect foothold in the world's largest diamond producer, De Beers.
Anglo owns De Beers.
Sources with direct knowledge of the development said however that Agarwal is not inclined to take over the entire Anglo American despite becoming the largest shareholder.
They said he is also not interested in getting a position on the Board of Directors and would continue to remain as an investor.
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In a statement, Volcan Investments, the family trust of the chairman of diversified miner Vedanta, said it intends to to acquire shares of 1.25 billion to 1.5 billion pounds (USD 2 billion), in addition to the 2 billion pounds spent in March on acquiring a 12.43 per cent holding.
"We are encouraged by the performance of Anglo American since our original investment earlier this year," Volcan Investment said. "The company has made good progress in its operational and financial performance and remains an attractive investment for our family trust."
Anglo American is one of the world's top five mining groups, alongside BHP Billiton, Rio Tinto, Vale and Glencore and has copper mines in Chile, iron ore operations in Brazil and South Africa as well as De Beers, the iconic diamond producer.
An indirect foothold in De Beers would increae Agarwal's presence in one more commodity after zinc, aluminium, iron ore, copper, power, silver and lead.
The diamonds sold by De Beers to its clients trickles down to the secondary market in Surat and Mumbai, where they are sold to small and medium diamantaires and even big companies.
India's diamond production is almost negligible and it is the largest consumer of rough diamond in the world, importing 80 per cent of total world production with an import bill of about USD 15 billion.
In a statement, London-listed Vedanta Resources said the proposed investment is being made by Volcan alone, and that the company is not participating in this investment.
Vedanta has made significant progress on its strategic priorities over the last year, including completion of the Vedanta Ltd-Cairn India merger, ramping up production from its portfolio of low cost assets, increasing free cash flow, and optimising its balance sheet through two successful liability management exercises in January and August 2017, respectively.
"The independent directors of the company (who for these purposes did not include the Executive Chairman Anil Agarwal or Executive Vice Chairman Navin Agarwal) have consented to the proposed investment pursuant to the Relationship Agreement between, among others, Volcan and the company," it added.
De Beers, the world's leading diamond exploration, mining and marketing company, producing over 30 million carats of diamonds per annum, 35 per cent of global rough diamond production.
Anglo, which is listed on the London and Johannesburg stock exchanges, has revenue of USD 23 billion, EBITDA of USD 6.1 billion and market cap of USD 20 billion. Its operations extend across Southern Africa, North and South America, Australia, Asia and Europe and employs 113,000 employees worldwide.