At the moment, the sovereign wealth fund holds the majority stakes in China's largest banks.
By ridding itself of the shares, restrictions on CIC's American investments would be liberated, allowing it to pump money into real estate deals, bonds and equities, reports the Financial Times.
According to unnamed sources, the move is being pushed by Wang Qishan, the Chinese vice-premier with a responsibility for finance.
If CIC does receive payment on its bank shares, it will be able to double the amount of cash it has to invest.
When CIC was established in 2007, the bank stakes were valued at about $70 billion.
Last month, China's vice-president Xi Jinping told AP that the country is seeking to establish a free trade deal with Australia.
He said the move would be in the "fundamental and long-term interests" of both nations.
By Gary Cooper