Executives of Washington's thrid largest banking company, Financial General Bankshares Inc., revealed for the first time yesterday that they are negotiating to sell out to a group of Middle Eastern investors led by the former head of Saudi Arabia's central intelligence agency.

But after weekend negotiating sessions involving some of Washington's most prominent deal-makers, the two sides failed to agree on price.

When the talks broke off on Sunday, they were discussing an offer of $28.50 a share -- a total of $150 million for the Financial General stock not already owned by the Middle Eastern group.

In a report to the Securities and Exchange Commission, attorneys for Sheik Kamal Adham of Saudi Arabia said the $28.50 was accepted by FG's top executives, Chairman B.F. Saul II, a real estate executive, and President J. William Middendorf II, a former secretary of the Navy.

Financial General attorney Martin Thaler, who participated in the talks, denied any offer was accepted. "The filing is not correct," said Thaler. "At no time was an agreement reached."

The publicly reported negotiations are the first sign of any settlement of the two-year fight for control of the $2.2 billion-asset company that owns 143 banking offices.

The talks were arranged by Dr. Armand Hammer, the international financier and chairman of Occidental Petroleum Co.

A member of Financial General's board and the owner of about 5 percent of its stock, Hammer set up a meeting last Friday between Saul and Middendorf and Adham's attorneys, Clark Clifford and Robert Altman.

Financial General issued a statement saying discussions had been held but "no agreements were reached and no arrangments or understandings exist among the parties."

Adham's group has been trying to buy control of Financial General since December 1978 when it secretly bought 18 percent of the company's stock with the help of former White House budget director Bert Lance.

Ordered by the Securities and Exchange Commission to make a public offer to buy all of Financial General or to sell out, the Adham group has been trying for two years to make that offer.

The bid has been blocked by a series of legal maneuvers that have made the Financial General case the longest, most costly bank control battle ever.

The negotiations last weekend parently were started in hopes of settling the issue before the Financial General stockholders meeting next Tuesday. Adham has nominated three rival candidates for the board of directors and is asking stockholders to pass a resolution calling on the company to drop its opposition to the takeover.

The talks are expected to continue and intensify as the meeting date nears.

Saul and Middendorf's negotiating position will be seriously weakened if the stockholders elect Adham's three board members and pass his resolution.

The banking company's largest single shareholder, Eugene B. Casey of Gaithersburg, said last week he would vote his 10 percent of the stock in favor of Adham's group. Counting Casey's shares, the Middle Eastern group controls somewhat more of the stock than Saul, Middendorf and others associated with the present management.

Adham, a close member of the Saudi royal family, heads a group that includes Faisal Saud al Fulaij, a businessman from Kuwait, and Abdullah Darwaish, who manages the financial affairs of the royal family of Abu Dhabi.

Details of the weekend meeting were disclosed in a report filed with the SEC and made public by Altman. Officials on both sides of the dispute refused to elaborate on their prepared statements.