According to a Financial Times report, OpenAI boss Sam Altman has said the move is the best way for the public to share in the upside of artificial intelligence.
Citing unnamed people close to the matter, the government and OpenAI are currently in early-stage "conceptual" talks.
OpenAI had been rumoured to go public on the Nasdaq this year, though its highly anticipated IPO may be pushed to 2027 as the company waits for current market volatility in the tech sector to ease.
Nevertheless, a 5% stake in the AI firm would be worth nearly $43bn, based on its most recent valuation of $852bn.
OpenAI's proposal is thought to be an attempt to appease government critics and clear political obstacles regarding potential future sector regulations, and comes just a month after rival Anthropic had to suspend its latest model due to national security concerns.
Altman, who has reportedly been pitching the idea to Trump for the past year, has proposed launching a sovereign wealth fund to hold similar stakes in other AI companies, though it is unclear at this stage whether any other firms are on board.
According to an OpenAI statement made in April, the idea of an AI public wealth fund could provide "every citizen – including those not invested in financial markets – with a stake in AI-driven economic growth”.