Although Federal Communications Commission Chairman Mark S. Fowler and Albert Halprin, chief of its common carrier bureau, vigorously deny rumors that they may be leaving, Commissioner Henry M. Rivera has made no secret of his job negotiations with outside law firms.

Sources inside the FCC say Fowler is "toying with reappointment," even though his term does not expire for more than a year. Commissioner Dennis Patrick's term ends in June, but he is expected to be renominated.

Rivera, a frequent dissenter in FCC decisions, said he is "beginning to examine the options available to me outside the commission," although his seven-year term does not expire until 1987.

Rivera said he has recused himself from FCC issues involving clients represented by the law firms with which he is talking. Those firms include Fisher Wayland Cooper & Leader; Paul Hastings; Janofsky & Walker and Gardner Carton & Douglas.

Members who are thinking about leaving the commission are required to disclose to Fred J. Goldsmith, chief of the Internal Review and Security Division, the law firms with which they are negotiating.

Bureau chiefs also are told so that notations can be made on proceedings and the commissioner excused from voting on the particular issue. However, an FCC spokesman said, "It's generally up to the commissioner" to notify the ethics officer and add or delete names of law firms.

Rivera, a Democrat and the first Hispanic to serve on the commission in its 50-year history, said he is leaving for personal reasons. But he was quick to criticize the FCC for not making more progress in a number of areas.

He said he wishes that more could be done on international issues, such as authorizing competition for the International Telecommunications Satellite Organization (Intelsat), a global consortium providing telecommunications services around the world; on the regulation of children's television programming; and in promoting minority ownership within the news media.

Rivera said he had tried to get approval for one commissioner to devote his efforts to working with the Commerce Department's National Telecommunications and Information Administration and the State Department to develop a comprehensive international communications policy. Rivera said he thought that Fowler was too busy and that "the agency would have been better served if he had delegated the assignment to one of us.''

Meanwhile Janice I. Obuchowski, legal assistant to the chairman for international policy, has consolidated the responsibility for the agency's international divisions.