President Reagan has approved new cuts in Medicare and Medicaid--and a proposed new tax on federal employes--that would reduce the likely budget deficit about $5 billion next year while requiring patients to pay a larger share of hospital and doctor bills, sources said yesterday.

The health proposals, which together will be a big chunk of the new budget cuts the president will propose to Congress next month, would radically alter federal health care policy in a variety of ways, shifting costs not only to elderly and needy patients, but to hospitals, private employers and state governments. As a result, the proposals are likely to meet sharp opposition on the Hill, where even Republicans have indicated they will be reluctant to vote many further budget cuts on top of those approved last year.

Reagan aides, however, say the deficit next year could exceed $150 billion if no further steps are taken to cut spending; health care programs, led by Medicare for the elderly and Medicaid for the poor, now make up a tenth of the budget.

Major health proposals approved by the president in the review process over the last two weeks include:

* Making federal employes pay that portion of the Social Security tax that finances Medicare; currently this is a 1.3 percent tax on the first $32,400 in pay. In return, federal employes would all become eligible for Medicare; the theory is that many of them qualify for it now, but on the basis of relatively few tax-paying years in private employment. This proposal would raise $650 million its first year.

* A 2 percent across-the-board reduction in federal reimbursements to hospitals for the care of Medicare patients. A hospital would compute the reimbursement to which it would be entitled under existing law, then be paid 2 percent less. This proposal would save the government an estimated $600 million to $800 million and replaced earlier proposals to issue new cost-containment regulations for specific reimbursement items.

* Making employers continue private health insurance coverage for those who keep working after 65, so that Medicare would not have to pay their bills.

* Allowing the states to charge low-income Medicaid patients for part of the costs of their basic services, for example, perhaps $1 or $2 a visit to a doctor and a few dollars a day for hospital care.

* Charging Medicare patients 10 percent a day for the second to the 60th day of hospital stays. At present, after a first-day payment of $260, the Medicare patient gets the second to 60th days free. The proposal would allow a payment of up to $26 a day for these days. This proposal would save enough money to allow the government to provide a new kind of "catastrophic costs" insurance, guaranteeing that a patient's out-of-pocket annual costs for all Medicare bills, both in hospital and out, would not exceed $2,500 (or under an alternative plan, $1,000). Even with the "catastrophic costs" provision, the proposal would save the government about $500 million a year.

* Allowing states to force the families of Medicaid patients in nursing homes to supplement what the government kicks in for the nursing home bills.

* Reducing by 3 percent the federal reimbursements to the states for the costs of optional services provided under Medicaid. Under this proposal, if the federal government normally reimburses a state for 60 percent of its Medicaid costs, it would continue to do so on basic services that states are required to provide under Medicaid law (such as hospital room and board, and laboratory and X-ray costs) but would give the state only 57 percent reimbursement for optional services such as eyeglasses, dental care and physical therapy. Another proposal would limit federal reimbursements for Medicaid administrative costs to 95 percent of the fiscal 1982 level.

* Limiting Medicare payments to radiologists and pathologists to 80 percent of normal charges; raising physicians' fee schedules under Medicare in October instead of July; holding such increases to about 5 percent in 1983 instead of 8 percent (this saves $450 million); indexing the Medicare premium charged patients to the cost of living each year; limiting doctor reimursements for services in outpatient departments and eliminating the Medicare subsidy for private hospital rooms; installing a special program to reduce Medicare hospital stays; and eliminating Medicare payments for certain non-covered services accidentally provided by hospitals or other service units.

The new cuts would be in addition to $2.5 billion already cut in fiscal 1982 through program changes approved in the budget reconciliation bill last summer.