Hill and Knowlton, a lobbying-public relations firm with a number of politically connected partners, is negotiating with Craig Fuller, former chief of staff to then-Vice President Bush, to take a major role in the company.

The negotiations, which remain unresolved, include two possible outcomes, said sources close to the negotiations. Hill and Knowlton may take on Fuller and merge with the lobbying-public relations firm that he currently heads, Wexler, Reynolds, Fuller, Harrison and Schule.

The second option would be for Fuller to leave his current firm, which would then remain in the hands of Anne Wexler, a Democrat and former assistant for public liaison to Jimmy Carter, and Nancy Clark Reynolds, a prominent Republican.

Fuller, 39, said, "We have been talking to Hill and Knowlton," but, he added, "We haven't done a deal, there is not one document signed, not one document has been presented to me to sign."

Several sources said that if the attempt to hire Fuller is successful, it would result in a reduction in the role of Robert K. Gray, who is currently chairman of Hill and Knowlton Public Affairs Worldwide. Gray was considered to be close to the Reagan White House.

Fuller and a number of others adamantly denied any prospective diminution in Gray's power at Hill and Knowlton. "Nowhere in any of these discussions is there any suggestion of anything that would have any impact on Robert K. Gray in his role as chairman of Hill and Knowlton USA and chairman of Hill and Knowlton Worldwide Public Affairs," one official said.

Hill and Knowlton, a 67-year-old national firm originally founded in Cleveland, has acquired a number of well-known Washington-area partners, including Gary Hymel, chief of staff to former House Speaker Thomas P. "Tip" O'Neill Jr., and Frank Mankiewicz, former press spokesman for the presidential campaign of George S. McGovern. Clients include American Airlines, General Electric Co. and Boeing Co.

After Bush's victory in 1988, Fuller lost out to New Hampshire Gov. John Sununu in a duel to become Bush's White House chief of staff.

The Wexler, Reynolds firm's clients include Aetna Life & Casualty, MCI Communications Corp. and Allied-Signal Inc.

The Washington lobbying-PR community has been undergoing a series of corporate consolidations and the joining of Hill and Knowlton with Wexler, Reynolds would be an extension of that process.

Hill and Knowlton is one of four firms either based in Washington or with a major presence in Washington all of which are controlled by the English firm WPP Group PLC.

The others include Timmons and Co., the partners of which include Republicans William E. Timmons and Tom C. Korologos and Democrats William Cable and Howard Paster; Ogilvy & Mather Public Affairs, which is chaired by Jody Powell, former Carter press spokesman; and Reese Communications Cos., run by Democrat Matthew A. Reese.