Forced to trim $118 million from its budget as a result of the Reagan administration's budget cuts, Amtrak is expected today to propose cutting back some of its nationwide passenger rail service.

Yet because the reductions are expected to be relatively minor, congressional sources yesterday indicated, Amtrak may encounter opposition from the Department of Transportation, which is seeking more significant service cuts.

The reductions are scheduled to be presented by Amtrak's management to its board of directors this morning. At that time, sources said Transportation officials may ask to delay any consideration of the proposed reductions. Transportation holds one of the 13 seats on Amtrak's board.

Agency officials were meeting late yesterday and declined to comment on what their position would be.

Industry sources said the cuts will involve less than a handful of routes,and these will be the lightly traveled ones.

Instead, these sources predicted, Amtrak will try to save money by reducing the frequencies of its train schedules on several routes.

For instance, Amtrak may trim at least one of the more than 30 runs it makes between Washington and New York, sources predicted.

Additionally, sources said Amtrak may change its daily Inter-American Chicago-Texas service to three-day-a-week service between St. Louis and its Texas points.

A possible target for more drastic change, however, may be The Cardinal, which runs between Washington and Chicago. The route may be reduced to run between Cincinnati and Chicago.

Sources said one possible route that may not survive is the lightly traveled Shenandoah, which goes from Washington to Cincinnati through West Virginia.

If approved, the cuts would take affect Oct. 1. Amtrak had sought a $853 million subsidy from the government for the next fiscal year, which begins this October. The Reagan administration sought to trim the subsidy to $613 million, but after a grass-roots campaign, Congress authorized a $735 million subsidy.