President Carter will soon propose a billion-dollar-a-year relief plan for the steel industry -- perhaps as early as tomorrow -- but first he must resolve a fundametal question that has sharply divided his top advisers.

That question is, what should the government demand from the steel industry in return for important environmetal concessions and substantial tax reductions?

Douglas Costle, head of the Environmental Protection Agency, has insisted all summer that if the administration gives the industry more time to meet clean air and water deadlines, it must have an iron-clad commitment that the money not spent in environmental compliance will be put into steel plant modernization, not into buying savings and loan institutions or oil properties or other attractive investments that have nothing to do with steel.

Steel company presidents have argued that their hands must not be tied, and they have found allies among Carter's economic advisers and Commerce Secretary Philip M. Klutznick, who feel the federal government is not equipped to tell the industry where and when to make its investments.

There is little argument that the steel industry needs help.

A high-level committee of industry, labor and government officials cochaired by Klutznick has agreed that the major U.S. steel makers will need to invest $4 billion to $5 billion a year for the next five years to catch up with leading steel makers in Japan and Western Europe, who benefit from more modern plants and from valuable government subsidies.

Over the horizon is the prospect of increasingly tough competition from steel producers in Mexico and other developing countries.

But the American steel industry, particularly some of the big steel companies that make the entire range of products from basic steel to specialized products, lacks the cash and credit to make the critically needed investments.

How much the Carter administration will offer the U.S. steel industry won't be known until the president discloses his plan. Carter is said to be impatient to go public with the steel plan, which could provide fresh ammunition for his presidential campaign.

The steel industry would be a major beneficiary of the business tax cuts proposed by Carter in his industrial revitalization plan; the cuts would total $53 billion between 1981 and 1983.

In addition, Costle, on EPA's behalf, has proposed that steel companies be given up to three years more time to meet clean air and clean water deadlines in order to ease the economic burden on the industry.

But Costle has insisted that he would ask Congress for legislation authorizing extended pollution control deadlines only if the delay results in accelerated capital investment in the steel industry.

Behind Costle's demand is EPA's concern over the amount of money the leading American steel companies have been spending on investments outside of steel making, and on dividend payments to shareholders.

The tripartite committee notes that the steel industry has paid generous dividends even as profits have declined -- in 1979, dividends totaled more than $600 million, or 46 percent of net after-tax profits, considerably higher than the dividend payment rate in growing industries that are investing heavily in new technology, industry analysts have noted.

Coupled with this is the industry's substantial investment -- about $500 million -- ain nonsteel activities, which last year accounted for about one-fifth of total investments.

A background paper on the steel industry prepared at the EPA this summer noted that the large steel companies have averaged only a 3 percent return on their steel operations, while making a 19 percent return on nonsteel activities.

To the steel industry, that contrast in earnings is a powerful argument for as hands-off policy by the government, letting the industry use the additional cash from tax breaks and environmental concessions as it sees fit. The result will be a healthier American steel industry, company leaders say.

The counterargument confronting Carer is that the tax concessions to the steel industry will have to be paid for somewhere, either in reduced federal spending or in higher tax payments by other companies and individuals.