By Gleb Bryanski

MOSCOW, April 21 (Reuters) - U.S. businessman James Cameron has offered to buy mining giant Eurasian Resources Group for $5 billion, a letter he sent to its board showed, as the company prepares to participate in a major expansion of Kazakhstan's rare earths output.

ERG, a Luxembourg-based producer of copper, cobalt, aluminium, and iron ore that is 40%-owned by the Kazakh government, said last year it had formed a task force to explore deposits of rare earth and rare metals in Kazakhstan.

Those minerals have gained particular attention in recent months as U.S. President Donald Trump's administration seeks alternatives to China to supply its domestic industry as a trade war between the countries escalates.

According to a source close to the company, talks between ERG and Cameron have been going on since the end of last year.

ERG, the Kazakh government, and Cameron, once a board chairman of former FTSE 250 mining firm Petropavlovsk, did not comment.

According to Cameron's letter to the ERG board, a copy of which was obtained by Reuters, Goldman Sachs is in preliminary talks to advise on the deal.

"The financing will come from a combination of my own funds, as well as equity contributions from other investors in the United States, and possibly Australia and the Middle East," the letter said.

Another source close to the transaction told Reuters the investor's interest in ERG is partly linked to Kazakhstan's potential in critical minerals exploration and mining. Kazakhstan aims to lift rare and rare earth metals output by 40% by 2028, with ERG seen taking a major role in the initiative.

This month, Kazakhstan's government announced that its geologists had discovered a large rare earth deposit with estimated resources exceeding 20 million metric tons.

Kazakhstan's Prime Minister Olzhas Bektenov said last year that data concerning the country's deposits of rare and rare earth metals, a state secret since Soviet times, is being gradually declassified.

If confirmed, this discovery could position Kazakhstan among the top three holders of rare earth reserves globally, following China and Brazil.

ERG once produced one-fifth of the world's gallium, a rare metal used in microchips and included on the U.S. list of critical materials. However, it ceased production after China increased its output of the metal in 2012.

Beijing in December banned gallium exports to the U.S. after a crackdown by Washington on China's chip sector.

In 2013, ERG was taken private in a $4.5 billion buyout by its three founders, who each owned approximately 20% of the company, along with the government.

Last month, one of ERG's founders and its board chairman, Kazakh-Israeli businessman Alexander Mashkevich, passed away, leaving only one of the original founders, Patokh Chodiev, among the current shareholders.

(Additional reporting by Mariya Gordeyeva in Kazakhstan; Editing by Guy Faulconbridge and Jan Harvey)

((gleb.bryanski@thomsonreuters.com;))