Citing Taiwanese military sources, the United Evening News report said Washington had made the request to acquire some 300 million 5.56-millimetre rifle bullets for an estimated $62 million.
The deal is yet to be finalised pending price negotiations, and - in line with its usual practice - Taiwan's defence ministry declined to comment on the report.
Taiwan produces some 400 million such bullets annually, according to the paper.
It added that most rifle bullets were manufactured by an arsenal in southern Kaohsiung, which has storage problems due to declining demand in the absence of any military conflict across the Taiwan Strait.
But it may be that Washington pays for the bullets in kind.
On Wednesday, the Pentagon agreed to sell air-to-ground Hellfire missiles worth $50 million to Taiwan to help the island defend itself against China.
"The US army has executed a letter of agreement with Taiwan, setting the stage for the sale of more than 400 AGM-114M blast-fragmentation Hellfire rounds under a foreign military sales contract," US defence giant Lockheed Martin said.
It would take the company about six months to make the Hellfire missiles ordered by Taiwan.
The missiles will be mounted on Taiwan's Super Cobra AH-1W attack and OH-58D Kiowa Warrior scout helicopters.