SAN FRANCISCO, FEB. 16 -- Physicist John Nuckolls, an advocate of President Reagan's Strategic Defense Initiative, has been selected to head the Lawrence Livermore National Laboratory, one of the nation's two nuclear weapons design centers, sources close to the selection process said today.

Nuckolls heads the lab's physics department, which oversaw development of some of the major concepts behind the controversial SDI program, informally known as "Star Wars." His appointment by University of California President David P. Gardner is subject to confirmation by the UC Regents, who are expected to consider the matter Thursday.

The university has managed the lab since it opened in 1952 under an agreement with the Energy Department, which funds it. Nuckolls would succeed Roger E. Batzel, 66, who is retiring after running the laboratory since 1971.

Nuckolls would head a lab of 8,000 scientists and other staff members with an annual budget of $1 billion. He will take over as many of the lab's top administrators are retiring and as U.S. and Soviet negotiators work toward arms-reduction treaties that could significantly affect the lab's work.

Nuckolls, who could not be reached for comment today, has worked at Livermore since 1955. He is said to be among the lab's foremost weapons designers.

He also is regarded as a close associate of physicist Edward Teller, father of the hydrogen bomb, one of Livermore's founders and one of the original proponents of the SDI.

"John has made his mark by forcing new questions," said Jay Davis, who works for him.

Nuckolls took over Livermore's physics department four years ago and reorganized it so that it was involved in new weapons research and experiments that have no immediate weapons application, Davis said.

Nuckolls has spoken of the need to press forward with energy research and advocates an international program to develop fusion power as a means of "inexhaustible" energy. The lab also conducts energy research.