Trustees of the Howard Hughes Medical Institute, which owns Hughes Aircraft Co., yesterday put the giant maker of missiles, satellites and electronic equipment up for sale, a transaction that analysts have said could be worth $3 billion.

The trustees said they had asked investment banker Morgan Stanley & Co. to "move forward with preparations" for either the sale of the company to another firm or a public offering of stock in Hughes Aircraft. The company's 68,000 employes could also wind up owning part of the company, under a long-sought employe-ownership plan.

"The next move is up to Morgan Stanley," said Donald Fredrickson, the president of the institute. "I can't put a timetable on it." Fred- rickson also said it was not yet known whether the company would be sold as a unit or broken up and sold piecemeal.

Based in El Segundo, Calif., Hughes Aircraft is one of the nation's top military contractors, with annual revenue estimated at more than $5 billion. It lately has been buffeted by charges that it did poor work on several government projects. Last summer, the Pentagon halted deliveries from the company on three important missile-building contracts, and the company voluntarily stopped delivery on radar systems for advanced Navy and Air Force fighters while it worked out quality-control problems. Shipments of the radar systems and some of the missiles have since resumed, and the company hopes to resume delivery on the rest of the contract work next month.

The prospective sale of Hughes Aircraft is another step in the sorting out of the tangled affairs of the late billionaire Howard Hughes, who founded the company and then set up the medical institute as its owner to avoid income taxes. Profits from the company are used to fund the institute's research into genetics, immunology and endocrinology.

Hughes was the institute's sole trustee, giving him tight rein over the company. But upon his death in 1976, control of the company became embroiled, as did most of Hughes' affairs, in legal disputes.

The key challenge came from officials in Delaware, where both the company and institute are incorporated. They argued that the company was not paying enough in income to the nonprofit institute; in 1983, the last year for which figures are available, Hughes Aircraft paid just $51 million in profits to the institute despite revenue of $4.9 billion.

The state and a relative of Hughes also charged that a group of Hughes' associates had taken control of the institute, and thus the company, without proper authority after the billionaire's death. That case turned on a disputed one-sentence change in the institute's bylaws allegedly added by Hughes in 1971, despite his longtime opposition to such a change.

The controversy was settled earlier this year when a Delaware state judge ruled the questionable clause invalid and ordered the appointment of a new board of nine trustees. The new trustees, including such businessmen as former E. I. du Pont de Nemours & Co. Inc. chairman Irving S. Shapiro, were to manage the institute's affairs and decide how best the investment in Hughes Aircraft could produce income for the institute. Fredrickson said yesterday that Morgan Stanley had been advising the board since September on possible options.