The Saudi Arabian government has agreed to buy the Peoples Life Insurance Co. headquarters building near the Watergate for use as a chancery.

The company would not disclose the price, and no one at the Saudi embassy could be reached for comment late yesterday.

The five-story, 99,499-square-foot building at 601 New Hampshire Ave. NW is being vacated by Peoples as part of a consolidation drive by its parent, Capital Holding Corp., of Louisville. Capital is combining the operations of Peoples with those of a related firm and moving them to Durham, N.C.

The Saudis' chancery is currently at 1520 18th St. NW.

A spokesman for Peoples said the sale of the building is contingent upon approval by the State Department, which under a law passed last year must approve all real estate purchases by foreign governments, and upon permission from the city zoning authorities.

A spokesman at State said that the department would have no objection to the sale, but the situation with the city was less clear.

Passage of the Foreign Missions Act last year has compelled the District to rewrite its zoning procedures for diplomatic property, and the new regulations have not yet been drawn up. Consequently, according to an official of the city zoning office, "there is no process by which the Board of Zoning Adjustment can process application."

The official noted that all diplomatic zoning applications that had been pending before the Foreign Missions Act became effective last October, "have been returned to the applicants." He said he had no idea when the regulations might be ready, noting that the first public hearing on them is scheduled for April 11.

This official added, however, that the building is zoned SP-2, and under the statute chanceries are to be permitted in the SP zone unless specifically disapproved by the BZA.

Peoples said it anticipates closing the sale "in the fourth quarter of 1983." Another city official said he "wouldn't want to guess" whether the District's zoning procedures will be in place by then.

The zoning turmoil has also caused problems for the Japanese embassy, which wants permission to expand its chancery on Massachusetts Avenue NW but has been unable to obtain the necessary approvals. The State Department has been pressing the city to speed the regulations, but the city contends that the issue is complicated, and the rules need to be written very carefully.

Peoples, founded in 1903, is one of the oldest businesses in the District. Its move to North Carolina has stirred considerable dismay among its 395 employes here, and although the company has said it plans to offer most of them jobs in Durham, a spokesman said when the move was announced in January that "we can assume that not all of them would accept."