Carter administration proposals for trimming money-losing passenger trains operated by Amtrak that are scheduled to be announced next week would eliminate about 10,000 miles of the passenger system's 27,000-mile national network.

Although Department of Transportation planners have not completed a final proposed Amtrak map, DOT Secretary Brock Adams will propose a "much smaller" rail passenger network at a luncheon in New York next Wednesday, government sources said yesterday.

DOT officials are behind schedule now in finishing their recommendations, which one source described as evidence of a "tight dilemma" the administration faces in proposing cut backs of service in districts represented by key members of Congress -- which ultimately must vote on the Carter plan.

According to a trade publication, Travel Management Daily, the final DOT plan will cut out more long-distance trains than proposed in a preliminary report last year.

Carter and Adams are on record as favoring a reduction in federal subsidies for Amtrak, which have exceeded $3 billion since 1971 when the government-sponsored corporation was established to maintain a skeleton intercity passenger network.

The final remaining overnight passenger train operated by a private company, Southern Ralway's Crescent, is scheduled to cease operations next Wednesday, and Amtrak will take over the train the following day.

Ironically, the Southern Cresent's future has been a major problem for DOT planners. Until recently, the Crescent was deleted from the proposed final system. But that would eliminate the only passenger service to Atlanta, the major city in Carter's home state, as well as to six other major southern cities.

Sources said the president has not advocated retention of the Crescent but if it survives in the final plan -- now considered possible -- that will require additional cutbacks of other long-distance trains, possibly by reducing frequency of some trains to two or three times a week. Southern was losing some $7 million a year in operating its one remaining passenger train.

Other trains scheduled to be halted in DOT planning to date include the Floridian between Chicago and Florida, the Inter American from Chicago to Loredo, the Lone Star between Chicago and Houston, and the Pioneer between Salt Lake City and Seattle.

Two western trains, the San Francisco Zephyr and Southwest Limited, would be combined in one Chicago-Kansas City-Denver-San Francisco routes. Three trains through West Virginia, including the Blue Ridge used by Washington commuters from Maryland and the Harper's Ferry area, also would be dropped.

Given current service levels, Amtrak's annual operating deficit is projected to mushroom to $1 billion or more by the early 1980s. The administration wants to trim that to about $800 million, and the budget proposed for fiscal 1980 would cut operating subsidies to $552 million compared with an authorization of $760 million.

Adams also will call for a boost in Amtrak fares, which now cover only about 37 cents of every dollar of cost.