Two rocket manufacturing companies have told NASA they intend to propose sites in Utah or Alabama for building the next generation of the space shuttle booster rocket.

Morton Thiokol Inc., which builds all the current shuttle boosters, said it wants its site near Brigham City, Utah, to be considered for the improved rockets, which are expected to be introduced in the next decade.Hercules Inc. of Magna, Utah, together with Atlantic Research Corp. of Gainesville, Va., proposed a site eight miles west of Montgomery, Ala.

At stake are a $1.2 billion plant and the employment a contract would bring for a decade or more. The advanced rockets are expected to arrive in the mid-1990s and replace the current boosters completely in 1997.

The National Aeronautics and Space Administration announced in April that it would issue a request for proposals this month or next from private industry to make the rocket in a new government-owned facility to be built on a government-owned site.

However, NASA said Friday that companies also were told they could submit an optional proposal for a privately owned rocket facility to be located on a site of the company's choice. Interested companies were given until May 31 to notify NASA if they want to pursue that course.

As a result, NASA said, it received the responses from Thiokol and Hercules-Atlantic Research.

"When the official request for proposals is issued, a government site will be specified as a tentative location for all companies to use as a common basis for proposals," NASA said. "The option of submitting an additional proposal for a privately owned facility will now be open only to Hercules-Atlantic Research and Morton Thiokol."

Three government owned sites are being evaluated, NASA said. They are at NASA's Kennedy Space Center in Florida, the Stennis Space Center in Bay St. Louis, Miss., and a Tennessee Valley Authority property known as the Yellow Creek site, in northeastern Mississippi.