Discontinuance of the Floridian, a daily passenger train between Chicago and Miami and St. Petersburg, will be recommended this week by Amtrak's management.

The decision comes after a series of hearings held along the train's route by Amtrak, the government-subsidized national rail passenger corporation. If Amtrak's board supports the proposal, at a meeting here Wednesday, the train probably would be cancelled a month later.

Coupled with a recent statement by Southern Railway president L. Stanley Crane, the Amtrak move could point to considerably reduced passenger train service in the Southeast states. Citing as estimated loss of $7 million this year, Crane said Southern may soon seek to drop its Southern Crescent between Washington, Atlanta, and New Orleans.

The Floridian, which stops at Nashville, Birmingham and Montgomery, has been operating at an annual loss of nearly $10 million. The daily train carried 162,715 riders in 1976 and 116,250 riders in the first eight months this year.

A recommendation to drop the train was revealed in a letter sent on Wednesday to members of Congress by Amtrak's vice president for government affairs, Bruce Pike.

In the wake of a decision by congressional conferees, providing supplemental appropriations of $3 million for the current fiscal year instead of the $56.5 million needed to continue all trains. Amtrak is faced with the need to cut down on train service.

Because of the time involved in planning route restructuring, however, Amtrak officer said they need six months before trains other than the Floridian can be earmarked for cancellation. Thus, Pike said, Amtrak must make cuts next spring to reduce costs by $60 million on an annual basis.

Pike said in his letter that the current two trains between Chicago and the Pacific Northwest could be consolidated into one or both could be dropped; and that service between Chicago and California could be combined on fewer trains.

Among other trains being studied for possible discontinuace is the daily National Limited between New York and Washington and Kansas City.