The Reagan administration is considering a plan to broaden Medicare to cover so-called catastrophic illnesses while possibly also requiring private employers to include catastrophic coverage in group insurance policies for their employes, according to government and health industry sources.

As now envisioned, the extra Medicare coverage would be financed by an increase in premiums so it would not add to the government's costs.

At the same time, the sources said, the administration is considering resubmitting to Congress several proposals rejected before that are aimed at reducing health-care costs -- now about one-tenth of the budget -- and help bring down the federal deficit. Among these deficit-reducing ideas are:

* A plan under which Medicare recipients could opt out of the program and buy private health insurance instead; they would be offered vouchers to defray the cost.

* A requirement that private health insurance companies reimburse the government when their policyholders are cared for in government hospitals; the government pays for this now.

* A requirement that workers count as income and pay federal income taxes on employer-paid health insurance premiums if they exceed a specified amount.

* Extending in some form the current "freeze" on increases in payments to physicians under Medicare.

* Reducing the federal income tax deduction for medical expenses.

* Eliminating Medicare reimbursements to hospitals for medical education for interns, residents and physicians.

* Raising the existing Medicare premium.

These proposals, which are being considered by high White House policy aides for possible inclusion in the fiscal 1986 budget, have not been approved by the president. They come at a time when the White House is searching for ways to reduce an anticipated $206 billion deficit without cutting defense or Social Security or raising taxes.

A relatively small number of Americans each year suffer catastrophic illnesses, such as prolonged treatment for cancer or stroke, which costs tens of thousands of dollars beyond the amount covered by insurance.

Many medical insurance policies cover medical costs only up to a certain amount; everything beyond that figure must be borne by the patient.

Conservatives have tended to favor catastrophic insurance to provide more benefits for the seriously ill while requiring the patient to bear costs of routine care.

Sources said the premium for a new Medicare catastrophic insurance proposal would likely cover only the added costs of the catastrophic coverage, and would not be used to bring in additional revenue to prop up other portions of the system.

They said the proposal being studied would cover Medicare hospital costs, but it has not been decided if it would also cover doctor bills or private insurance policies.

They said one option might be a proposal last year by the Social Security Advisory Council: guarantee every Medicare patient up to 365 days of hospital care annually upon payment of the existing $356 fee for the first day. At present, only the first 60 days are free.

To pay for the added costs of providing the extra days of care free, Medicare either could charge each of the 30 million enrollees an annual fee (the advisory council gstimated this would be $56 a year) or charge the 7.5 million persons who go to the hospital each year some surcharge for the first day, or first 10 days.

The average Medicare stay in a hospital is 11 days.

The sources said the administration is considering including a provision requiring private employers to include catastrophic protection in their policies for their workers, perhaps by denying them tax deductions for the premiums they pay if their policies do not include catastrophic protection.

Only 61 percent of the population under 65 covered by private health plans has medical and hospital catastrophic protection.

Under the Medicare voucher proposal, any enrollee could receive a voucher from the government, worth the insurance value of Medicare coverage, and buy his own policy from a private insurer. The voucher amount would be increased for inflation each year, but would not go up as fast as anticipated program costs, so the government would eventually save money.

Under the governmental hospital proposal, if an individual with private insurance (such as a veteran with non-service-connected disabilities) received treatment in a military or veterans' hospital, the government could seek payment from the insurance company.

At present, private policies do not pay for treatment in a military or Veterans Administration hospital.

Under the health insurance tax proposal, as submitted last year, employer-paid health insurance premiums exceeding $175 for a family or $70 a month for an individual would have been treated as income to the worker and made subject to income tax. This would raise $40 billion over five years.

Also under study is a plan to have Medicare stop paying a share of the costs of medical education in hospitals; savings to Medicare could be as much as $3 billion a year.

Some sources said the administration was considering two proposals rejected by Congress last year: raising the Medicare doctor insurance premium over several years to cover 35 percent of the program's cost instead of 25 percent.