Stanford University trustees today unanimously approved a site for the proposed Reagan presidential library.

Robert Freelan, head of the university's planning committee, said he expects that President Reagan will make a "fairly expeditious" decision on the site.

Presidential counselor Edwin Meese III, who recently viewed the 20-acre site in the foothills adjacent to the university's main campus, told university officials in a letter that the White House would like to preserve "as much of the natural environment as possible."

Meese also said Reagan "strongly prefers" the existing architecture of the Stanford campus, where red-tiled roofs predominate.

If Reagan approves the site, as expected, an independent fund-raising foundation is to be formed, an architect selected and approval sought from various government agencies.

In the wake of campus controversy, the White House last year withdrew a proposal to combine the library with a Ronald Reagan Public Affairs Center, which would have been administered by the Hoover Institution on War, Revolution and Peace, Stanford's political think tank.

No cost estimate has been made for the library, which is to house presidential papers and a small exhibition area footage be used for exhibits. Meese said in his letter that "we do not intend to promote the library as a tourist attraction."

Other Reagan papers and memorabilia are housed at the Hoover Institution and at his alma mater, Eureka College in Eureka, Ill.