The plan is similar to a Republican proposal passed by the House last year and debated by the Senate, said officials who are working on the plan with Mr. Bush.
It would allow current beneficiaries and those close to retirement to remain in the traditional fee-for-service Medicare program, but it would include inducements for them to join a private plan.
The inducements would include drug coverage and a new provision covering catastrophic medical costs. The plan, first reported by The Washington Post and The New York Times, is not final because key decisions remain to be made, officials said.
Mr. Bush plans to devote a section of next Tuesday's State of the Union address to health care, and will outline the principles of his Medicare and prescription drug plans Wednesday in Michigan.
But final details of the package won't be nailed down next week, officials said.
According to The New York Times, a recent description of the proposal in government documents envisions "no prescription drug coverage" for people in traditional fee-for-service Medicare.
More than 85 percent of the 40 million Medicare beneficiaries are in the fee-for-service program.
The issue for the administration, reports CBS News White House Correspondent Dan Raviv, is cost control.
The plan strives to slow the growth of Medicare costs over the coming decades by attracting patients into what administration officials hope will be a less expensive system dominated by health maintenance organizations and other private health plans.
Medicare beneficiaries would have three options — the existing fee-for-service benefits, HMOs with drug benefits and private plans offering "enhanced fee-for-service benefits," according to the Times report in Friday's editions.
The plan would be phased in over a period of years and would perhaps take effect at different times in various parts of the country, depending on how successful the government is at persuading private health plans to take part, the Post said.
Administration officials told the Times early estimates indicate that the drug benefits in the proposal would cost $388 billion over 10 years.
Private health plans would make bids each year, detailing a price they would charge for the package of goods and services covered by Medicare. The government would choose three of the lowest bidders in each of 10 geographic regions, the Times said.
According to the American Association of Retired Persons, senior citizens comprise only 12 percent of the U.S. population but represent 40 percent of the prescription drug market.
Last summer's Senate debate over prescription drug benefits stalled over the issue of private sector involvement. Most Republicans wanted to subsidize private companies to administer the benefit, while most Democrats wanted direct control by Medicare. There was also disagreement over who should be covered.