Is a Japanese company involved in the illegal sale of submarine propeller-milling machinery to the Soviets about to find a friend high in the Reagan administration: Defense Secretary-designate Frank C. Carlucci?

This is the question that engrossed investigators for Sen. Sam Nunn (D-Ga.), chairman of the Armed Services Committee, as they prepared for confirmation hearings on Carlucci.

The question arises out of our stories about the involvement of the huge Japanese trading company, C. Itoh, in the illegal sale to the Soviets. Carlucci had been a business associate of C. Itoh, and was President Reagan's national security adviser when the submarine-propeller scandal broke.

C. Itoh, whose spokesman claims it is the world's biggest trading company, acted as a sort of middleman in the illicit sale by Toshiba Machine Co. of machines that can make Soviet submarines much more difficult to detect. It was one of the most serious breaches of Western security in years, and it has been estimated that countermeasures to overcome the $17 million sale could cost the United States $30 billion.

C. Itoh insists it did not know that sensitive military technology was involved in the sale.

The Senate investigators' attention is focused on a now-defunct trading arm of Sears, Roebuck called Sears World Trade. Carlucci headed the firm before he was named national security adviser in the wake of the Iran-contra arms scandal last year.

The first head of Sears World Trade was Roderick M. Hills, a former Securities and Exchange Commission member who told us he has "had dealings" with C. Itoh since at least the 1960s. In the fall of 1981, Sears asked him to form a new international trading company, and his first move was to take corporate executives to Asia for a two-week visit, which included a formal luncheon in Tokyo with C. Itoh's top people.

Hills said he recommended that the new Sears unit enter into partnership with C. Itoh, and Sears brass agreed.

Hills said he was eager to hire old Washington hands for the new Sears enterprise, and in 1982 he persuaded Carlucci, a veteran bureaucrat, to resign as Caspar W. Weinberger's deputy at the Defense Department and join Sears World Trade as president and chief operating officer.

Hills resigned as Sears World Trade chairman two weeks later, and on Sept. 19, 1984, Carlucci was promoted to chairman and chief executive.

In October 1986, Sears closed down Sears World Trade after $60 million in losses, and Carlucci went job hunting. Two months later, he replaced Vice Adm. John M. Poindexter as national security adviser.

From that strategic position, Carlucci watched this year as congressional fury erupted over Toshiba's sale (through C. Itoh) of propeller-milling machines to the Soviets. But as far as we know, he did not intervene, until Sen. Alan Dixon (D-Ill.) sponsored a bill that would punish C. Itoh and another company for involvement in the Toshiba deal.

At that point, both the National Security Council headed by Carlucci, and his former Sears boss, Hills, did their best to block the bill.