The board of directors of the National Capital Area YWCA, faced with financial problems, voted Thursday to authorize negotiations leading to possible relocation of the YWCA from 17th and K Streets NW, board sources said.

The board voted to authorize its real estate negotiators to begin discussions with makers of a reported $6.4 million offer for the landmark YWCA structure.

At the same time, sources said, the board authorized negotiations to buy the National Permanent Federal Savings and Loan Association building at 1400 St. NW for use as a new building.

Such an exchange of properties would presumably be financially advantageous because real estate east of 15th Street is less costly than that to the west.

The present YWCA building probably would be torn down. The site at 17th and K Streets has been mentiond recently as a likely target for redevelopment.

If the G Street site were bought, it is expected that the building there would be renovated an an additional structure would be built on an adjoining parking lot, according to board sources.

Officials of the savings and loan could not be reached immediately for comment last night.

Asked to comment yesterday on the reported sale agreement, Mildred Savacool, executive director of the National Capital Area YWCA said only that the board had authorized the start of negotiations to sell.

In a fact sheet issued in May, the National Capital Area YMCA said it had been considering real estate options because of the YWCA's need to "find a way to balance its annual operating budget . . ."

According to the fact sheet, the operating budget "has had an average deficit of $50,000 for the last 7 1/2 years."

Another option considered, in addition to selling, was renovation of the present building, which is more than 50 years old.

After being told that renovation would cost between $1.4 and $2 million, the board reportedly rejected that option in February as "financially unfeasible."

"We would have been willing to renovate if somebody had come up with the $2 1/2 million necessary to do it," Savacool said yesterday.

"We have to maximize our financial resources. By doing so, we hope to provide our members with a plant that will provide all the program space we need. We're committed to staying in the center of the city and to serving women there," she said.

According to board sources, proposals for a new YWCA facility do not include a residence hall. The present building is actually tow connected structures - an activities building and a residence hall.

Instead of a separate gymnasium and recital hall as in the present building, proposals provide for a multipurpose room in the new structure. A pool is under consideration but, according to the fact sheet, more information is needed about its economic feasibility.

In January, 1976, the board of managers of D.C. branch of the YWCA voted to keep the branch at 17th and K Streets. Board officers could not be reached immediately for comment last night.

Some National Capital Area board members have suggested that rehabilitation of the present site, used by thousands of persons yearly, might have been done in stages as funds became available.