BEIJING—The maker of China's new stealth fighter jet has teamed up with a tiny, unprofitable California company to try to launch bids for U.S. defense contracts, possibly including one to supply Chinese helicopters to replace the aging Marine One fleet used by the president, according to people involved in the partnership.

Any Chinese bids for this or another contract under discussion would be certain to meet intense political resistance and would appear to have very little chance of success given mounting U.S. concern about...