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Stephen Feinberg, the billionaire financier who owns the military contractor DynCorp International, is informally advising Trump on Afghanistan, according to a report in The New York Times, which said the company may potentially play a role in safeguarding American mining operations.

"We have no expectation of supporting commercial mining programs, but continue to work at the direction of the U.S. government," a DynCorp representative told CNBC. DynCorp has operated in Afghanistan since 2003, providing aviation, logistics, training, intelligence and operational solutions where needed.

Yet while Trump is looking at the possibility of the U.S. cashing in on the poor war-torn country, others have already started. Northern Afghanistan is rich with natural gas reserves and has attracted Russia's attention for decades.

During the Soviet invasion, Russia laid the framework to control Afghanistan's natural gas but abandoned the effort after the Taliban seized control of the country.

Last month, Afghan President Ashraf Ghani spoke with German President Frank-Walter Steinmeier about lithium deposits in Helmand province, which could be put to work by European companies. The element is a key ingredient in rechargeable batteries used in smartphones and electric cars, and for its part Germany is eyeing Afghan lithium for its automobile industry.

Elsewhere, China has taken the lead in exploring its neighboring country's natural resources. In February, CNBC reported that China's Metallurgical Group Corporation (MCC) is planning to extract $100 billion worth of copper from Afghanistan. Back in 2007, the company leased land near Kabul for $3 billion.

At one point, the Taliban had given the project a green light. However, the project has been delayed because archaeologists discovered a 5,000-year-old Buddhist city in the exact location that holds the world's second-largest copper deposit.

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At stake in US military efforts to stabilize Afghanistan: At least $3 trillion in natural resources - CNBC